正整数A×颠倒数(A)=正整数B×颠倒数(B)

王守恩

正整数A×颠倒数(A)=正整数B×颠倒数(B)。

譬如：144×441=252×252,   168×861=294×492。

请搜索计算更多这样的数，提交一个序列。

northwolves

1. f[n_]:=(m=IntegerReverse@n;If[m>=n,{m*n,n,m},{}]);
   
2. s=Select[Table[f[n],{n,10000}],#!={}&];
   
3. t=Select[Gather[s,First@#1==First@#2&],Length@#>1&]// Grid

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{63504,144,441}        {63504,252,252}
{101556,156,651}        {101556,273,372}
{144648,168,861}        {144648,294,492}
{185472,276,672}        {185472,384,483}
{5166504,1224,4221}        {5166504,2142,2412}
{7812756,1236,6321}        {7812756,2163,3612}
{10509408,1248,8421}        {10509408,2184,4812}
{8262306,1326,6231}        {8262306,2613,3162}
{12494209,1339,9331}        {12494209,3193,3913}
{5955264,1344,4431}        {5955264,2352,2532}
{8856036,1356,6531}        {8856036,2373,3732}
{11807208,1368,8631}        {11807208,2394,4932}
{11768148,1428,8241}        {11768148,2814,4182}
{9523696,1456,6541}        {9523696,2743,3472}
{6794424,1464,4641}        {6794424,2562,2652}
{9949716,1476,6741}        {9949716,2583,3852}
{13564768,1568,8651}        {13564768,2954,4592}
{7683984,1584,4851}        {7683984,2772,2772}
{10865686,1586,6851}        {10865686,2873,3782}
{11093796,1596,6951}        {11093796,2793,3972}
{14201712,2316,6132}        {14201712,3504,4053}
{19164096,2328,8232}        {19164096,4074,4704}
{15089472,2346,6432}        {15089472,3264,4623}
{22818208,2369,9632}        {22818208,3296,6923}
{15449112,2436,6342}        {15449112,3624,4263}
{20666016,2448,8442}        {20666016,4284,4824}
{16746912,2556,6552}        {16746912,3744,4473}
{22218336,2568,8652}        {22218336,4494,4944}
{17393152,2576,6752}        {17393152,3584,4853}
{24706318,2639,9362}        {24706318,3926,6293}
{18095112,2676,6762}        {18095112,3864,4683}
{19493712,2796,6972}        {19493712,3984,4893}
{29973924,3468,8643}        {29973924,4386,6834}
{29116584,3528,8253}        {29116584,4716,6174}
{30873024,3648,8463}        {30873024,4836,6384}
{32679864,3768,8673}        {32679864,4956,6594}
{41478016,4439,9344}        {41478016,6176,6716}
{45121216,4669,9664}        {45121216,6496,6946}

northwolves

改成这样就可以了：

1. Union@@@Select[GatherBy[Select[Table[m=IntegerReverse@n;{If[m>=n,m*n,0],n},{n,100000}],#[[1]]>0&],First],Length@#>1&]

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王守恩

northwolves 发表于 2025-2-22 19:32
改成这样就可以了：

{144, 252, 63504}, {156, 273, 101556}, {168, 294, 144648}, {276, 384, 185472}, {1224, 2142, 5166504}, {1236, 2163, 7812756}, {1248, 2184, 10509408}, {1326, 2613, 8262306}, {1344, 2352, 5955264}, {1356, 2373, 8856036},
{1368, 2394, 11807208}, {1428, 2814, 11768148}, {1456, 2743, 9523696}, {1464, 2562, 6794424}, {1476, 2583, 9949716}, {1568, 2954, 13564768}, {1584, 2772, 7683984}, {1586, 2873, 10865686}, {1596, 2793, 11093796}

第3个数是可以去掉的。第2个数是与第1个数有联系, 光凭第1个数怎么把第2个数拉出来？光凭第1个数能把第2个数拉出来吗？再想想。

第2个数也去掉——144, 156, 168, 276, 1224, 1236, 1248, 1326, 1339, 1344, 1356, 1368, 1428, 1456, 1464, 1476, 1568, 1584, 1586, 1596, 2316, 2346, 2369, 2436, 2556, 2576——OEIS没有这串数。挺诱人的！

northwolves

王守恩 发表于 2025-2-23 09:13
{144, 252, 63504}, {156, 273, 101556}, {168, 294, 144648}, {276, 384, 185472}, {1224, 2142, 5166504 ...

1. s = Union @@@
   
2.   Select[GatherBy[
   
3.     Select[Table[
   
4.       m = IntegerReverse@n; {If[m >= n, m*n, 0], n}, {n,
   
5.        100000}], #[[1]] > 0 &], First], Length@# > 1 &]; t =
   
6. s[[All, 1]]

复制代码

northwolves

光凭第1个数怎么把第2个数拉出来
-----------------------------------------
筛选即可

1. f[n_] := (m = n*IntegerReverse@n;
   
2.   Select[Range[n + 1, Sqrt[m]], #*IntegerReverse@# == m &]);
   
3. a = {144, 156, 168, 276, 1224, 1236, 1248, 1326, 1339, 1344};
   
4. f[#] & /@ a // Flatten

复制代码

{252, 273, 294, 384, 2142, 2163, 2184, 2613, 3193, 2352}

王守恩

northwolves 发表于 2025-2-23 09:54
光凭第1个数怎么把第2个数拉出来
-----------------------------------------
筛选即可

正整数A×颠倒数A=正整数B×颠倒数B。

譬如：144×441=252×252。

譬如：168×861=294×492。

我们不妨约定A是最小的那个。

这串数就是A——144, 156, 168, 276, 1224, 1236, 1248, 1326, 1339, 1344, 1356, 1368, 1428, 1456, 1464, 1476, 1568, 1584, 1586, 1596, 2316, 2346, 2369, 2436, 2556, 2576,

凭这个A——可以有颠倒数A——可以有A×颠倒数A的积——可以有B×颠倒数B的积——可以有B。 光凭A怎么把B拉出来？光凭A能把B拉出来吗？我心里没底。

凭A能把B拉出来。这串数就完整了。题目简单, 思路清晰。可以去OEIS。OEIS没有这串数。挺诱人的！

nyy

1. Clear["Global`*"];(*mathematica11.2,win7(64bit)Clear all variables*)
   
2. fun[n_]:=Module[{ra,cj,aa,bb,cc,dd},
   
3.     ra=FromDigits@Reverse@IntegerDigits[n];(*得到n的颠倒数*)
   
4.     cj=n*ra;(*获得乘积*)
   
5.     aa=Divisors[n*ra];(*获得因子*)
   
6.     bb=Select[aa,And[#<=Sqrt[cj],#!=n,#!=ra]&];(*获得乘积的因子,并且是较小的因子,既不等于n,又不等于ra*)
   
7.     cc=(#*FromDigits@Reverse@IntegerDigits[#])&/@bb;(*每个因子乘以颠倒数*)
   
8.     dd=Select[cc,#==cj&];(*选出乘积等于cj的*)
   
9.     If[Length@dd>0,True,False]
   
10. ]
    
11. aaa=Select[Range[1,10^5],fun[#]&]
    

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{144, 156, 168, 252, 273, 276, 294, 372, 384, 441, 483, 492, 651, \
672, 861, 1224, 1236, 1248, 1326, 1339, 1344, 1356, 1368, 1428, 1456, \
1464, 1476, 1568, 1584, 1586, 1596, 2142, 2163, 2184, 2316, 2328, \
2346, 2352, 2369, 2373, 2394, 2412, 2436, 2448, 2532, 2556, 2562, \
2568, 2576, 2583, 2613, 2639, 2652, 2676, 2743, 2772, 2793, 2796, \
2814, 2873, 2954, 3162, 3193, 3264, 3296, 3468, 3472, 3504, 3528, \
3584, 3612, 3624, 3648, 3732, 3744, 3768, 3782, 3852, 3864, 3913, \
3926, 3972, 3984, 4053, 4074, 4182, 4221, 4263, 4284, 4386, 4431, \
4439, 4473, 4494, 4592, 4623, 4641, 4669, 4683, 4704, 4716, 4812, \
4824, 4836, 4851, 4853, 4893, 4932, 4944, 4956, 6132, 6174, 6176, \
6231, 6293, 6321, 6342, 6384, 6432, 6496, 6531, 6541, 6552, 6594, \
6600, 6716, 6741, 6752, 6762, 6834, 6851, 6923, 6946, 6951, 6972, \
8232, 8241, 8253, 8421, 8442, 8463, 8631, 8643, 8651, 8652, 8673, \
9331, 9344, 9362, 9632, 9664}

nyy

1. Clear["Global`*"];(*mathematica11.2,win7(64bit)Clear all variables*)
   
2. fun[n_]:=Module[{ra,cj,aa,bb,cc,dd},
   
3.     ra=FromDigits@Reverse@IntegerDigits[n];(*得到n的颠倒数*)
   
4.     cj=n*ra;(*获得乘积*)
   
5.     aa=Divisors[n*ra];(*获得因子*)
   
6.     bb=Select[aa,And[#<=Sqrt[cj],#!=n,#!=ra]&];(*获得乘积的因子,并且是较小的因子,既不等于n,又不等于ra*)
   
7.     cc={#,(#*FromDigits@Reverse@IntegerDigits[#])}&/@bb;(*每个因子,以及每个因子乘以颠倒数*)
   
8.     dd={};(*先搞一个长度等于零的初始值*)
   
9.     dd=Select[cc,#[[2]]==cj&](*选出乘积等于cj的,第二个元素才是乘积*)
   
10. ]
    
11. aaa=Select[Range[1,10^4],Length@fun[#]>0&](*选出这些要求的数*)
    
12. bbb={#,fun[#]}&/@aaa(*得到数,与另外对应的数,以及乘积*)
    
13. Grid[bbb,Alignment->Left](*列表显示*)
    

复制代码

输出结果
{144, 156, 168, 252, 273, 276, 294, 372, 384, 441, 483, 492, 651, \
672, 861, 1224, 1236, 1248, 1326, 1339, 1344, 1356, 1368, 1428, 1456, \
1464, 1476, 1568, 1584, 1586, 1596, 2142, 2163, 2184, 2316, 2328, \
2346, 2352, 2369, 2373, 2394, 2412, 2436, 2448, 2532, 2556, 2562, \
2568, 2576, 2583, 2613, 2639, 2652, 2676, 2743, 2772, 2793, 2796, \
2814, 2873, 2954, 3162, 3193, 3264, 3296, 3468, 3472, 3504, 3528, \
3584, 3612, 3624, 3648, 3732, 3744, 3768, 3782, 3852, 3864, 3913, \
3926, 3972, 3984, 4053, 4074, 4182, 4221, 4263, 4284, 4386, 4431, \
4439, 4473, 4494, 4592, 4623, 4641, 4669, 4683, 4704, 4716, 4812, \
4824, 4836, 4851, 4853, 4893, 4932, 4944, 4956, 6132, 6174, 6176, \
6231, 6293, 6321, 6342, 6384, 6432, 6496, 6531, 6541, 6552, 6594, \
6600, 6716, 6741, 6752, 6762, 6834, 6851, 6923, 6946, 6951, 6972, \
8232, 8241, 8253, 8421, 8442, 8463, 8631, 8643, 8651, 8652, 8673, \
9331, 9344, 9362, 9632, 9664}

结果详细化
{{144, {{252, 63504}}}, {156, {{273, 101556}}}, {168, {{294,
    144648}}}, {252, {{144, 63504}}}, {273, {{156,
    101556}}}, {276, {{384, 185472}}}, {294, {{168,
    144648}}}, {372, {{156, 101556}}}, {384, {{276,
    185472}}}, {441, {{252, 63504}}}, {483, {{276,
    185472}}}, {492, {{168, 144648}}}, {651, {{273,
    101556}}}, {672, {{384, 185472}}}, {861, {{294,
    144648}}}, {1224, {{2142, 5166504}}}, {1236, {{2163,
    7812756}}}, {1248, {{2184, 10509408}}}, {1326, {{2613,
    8262306}}}, {1339, {{3193, 12494209}}}, {1344, {{2352,
    5955264}}}, {1356, {{2373, 8856036}}}, {1368, {{2394,
    11807208}}}, {1428, {{2814, 11768148}}}, {1456, {{2743,
    9523696}}}, {1464, {{2562, 6794424}}}, {1476, {{2583,
    9949716}}}, {1568, {{2954, 13564768}}}, {1584, {{2772,
    7683984}}}, {1586, {{2873, 10865686}}}, {1596, {{2793,
    11093796}}}, {2142, {{1224, 5166504}}}, {2163, {{1236,
    7812756}}}, {2184, {{1248, 10509408}}}, {2316, {{3504,
    14201712}}}, {2328, {{4074, 19164096}}}, {2346, {{3264,
    15089472}}}, {2352, {{1344, 5955264}}}, {2369, {{3296,
    22818208}}}, {2373, {{1356, 8856036}}}, {2394, {{1368,
    11807208}}}, {2412, {{1224, 5166504}}}, {2436, {{3624,
    15449112}}}, {2448, {{4284, 20666016}}}, {2532, {{1344,
    5955264}}}, {2556, {{3744, 16746912}}}, {2562, {{1464,
    6794424}}}, {2568, {{4494, 22218336}}}, {2576, {{3584,
    17393152}}}, {2583, {{1476, 9949716}}}, {2613, {{1326,
    8262306}}}, {2639, {{3926, 24706318}}}, {2652, {{1464,
    6794424}}}, {2676, {{3864, 18095112}}}, {2743, {{1456,
    9523696}}}, {2772, {{1584, 7683984}}}, {2793, {{1596,
    11093796}}}, {2796, {{3984, 19493712}}}, {2814, {{1428,
    11768148}}}, {2873, {{1586, 10865686}}}, {2954, {{1568,
    13564768}}}, {3162, {{1326, 8262306}}}, {3193, {{1339,
    12494209}}}, {3264, {{2346, 15089472}}}, {3296, {{2369,
    22818208}}}, {3468, {{4386, 29973924}}}, {3472, {{1456,
    9523696}}}, {3504, {{2316, 14201712}}}, {3528, {{4716,
    29116584}}}, {3584, {{2576, 17393152}}}, {3612, {{1236,
    7812756}}}, {3624, {{2436, 15449112}}}, {3648, {{4836,
    30873024}}}, {3732, {{1356, 8856036}}}, {3744, {{2556,
    16746912}}}, {3768, {{4956, 32679864}}}, {3782, {{1586,
    10865686}}}, {3852, {{1476, 9949716}}}, {3864, {{2676,
    18095112}}}, {3913, {{1339, 12494209}}}, {3926, {{2639,
    24706318}}}, {3972, {{1596, 11093796}}}, {3984, {{2796,
    19493712}}}, {4053, {{2316, 14201712}}}, {4074, {{2328,
    19164096}}}, {4182, {{1428, 11768148}}}, {4221, {{2142,
    5166504}}}, {4263, {{2436, 15449112}}}, {4284, {{2448,
    20666016}}}, {4386, {{3468, 29973924}}}, {4431, {{2352,
    5955264}}}, {4439, {{6176, 41478016}}}, {4473, {{2556,
    16746912}}}, {4494, {{2568, 22218336}}}, {4592, {{1568,
    13564768}}}, {4623, {{2346, 15089472}}}, {4641, {{2562,
    6794424}}}, {4669, {{6496, 45121216}}}, {4683, {{2676,
    18095112}}}, {4704, {{2328, 19164096}}}, {4716, {{3528,
    29116584}}}, {4812, {{1248, 10509408}}}, {4824, {{2448,
    20666016}}}, {4836, {{3648, 30873024}}}, {4851, {{2772,
    7683984}}}, {4853, {{2576, 17393152}}}, {4893, {{2796,
    19493712}}}, {4932, {{1368, 11807208}}}, {4944, {{2568,
    22218336}}}, {4956, {{3768, 32679864}}}, {6132, {{3504,
    14201712}}}, {6174, {{3528, 29116584}}}, {6176, {{4439,
    41478016}}}, {6231, {{2613, 8262306}}}, {6293, {{2639,
    24706318}}}, {6321, {{2163, 7812756}}}, {6342, {{3624,
    15449112}}}, {6384, {{3648, 30873024}}}, {6432, {{3264,
    15089472}}}, {6496, {{4669, 45121216}}}, {6531, {{2373,
    8856036}}}, {6541, {{2743, 9523696}}}, {6552, {{3744,
    16746912}}}, {6594, {{3768, 32679864}}}, {6600, {{528,
    435600}}}, {6716, {{4439, 41478016}}}, {6741, {{2583,
    9949716}}}, {6752, {{3584, 17393152}}}, {6762, {{3864,
    18095112}}}, {6834, {{3468, 29973924}}}, {6851, {{2873,
    10865686}}}, {6923, {{2369, 22818208}}}, {6946, {{4669,
    45121216}}}, {6951, {{2793, 11093796}}}, {6972, {{3984,
    19493712}}}, {8232, {{4074, 19164096}}}, {8241, {{2814,
    11768148}}}, {8253, {{4716, 29116584}}}, {8421, {{2184,
    10509408}}}, {8442, {{4284, 20666016}}}, {8463, {{4836,
    30873024}}}, {8631, {{2394, 11807208}}}, {8643, {{4386,
    29973924}}}, {8651, {{2954, 13564768}}}, {8652, {{4494,
    22218336}}}, {8673, {{4956, 32679864}}}, {9331, {{3193,
    12494209}}}, {9344, {{6176, 41478016}}}, {9362, {{3926,
    24706318}}}, {9632, {{3296, 22818208}}}, {9664, {{6496,
    45121216}}}}

结果列表化
\[\begin{array}{ll}
144 & \left(
\begin{array}{cc}
252 & 63504 \\
\end{array}
\right) \\
156 & \left(
\begin{array}{cc}
273 & 101556 \\
\end{array}
\right) \\
168 & \left(
\begin{array}{cc}
294 & 144648 \\
\end{array}
\right) \\
252 & \left(
\begin{array}{cc}
144 & 63504 \\
\end{array}
\right) \\
273 & \left(
\begin{array}{cc}
156 & 101556 \\
\end{array}
\right) \\
276 & \left(
\begin{array}{cc}
384 & 185472 \\
\end{array}
\right) \\
294 & \left(
\begin{array}{cc}
168 & 144648 \\
\end{array}
\right) \\
372 & \left(
\begin{array}{cc}
156 & 101556 \\
\end{array}
\right) \\
384 & \left(
\begin{array}{cc}
276 & 185472 \\
\end{array}
\right) \\
441 & \left(
\begin{array}{cc}
252 & 63504 \\
\end{array}
\right) \\
483 & \left(
\begin{array}{cc}
276 & 185472 \\
\end{array}
\right) \\
492 & \left(
\begin{array}{cc}
168 & 144648 \\
\end{array}
\right) \\
651 & \left(
\begin{array}{cc}
273 & 101556 \\
\end{array}
\right) \\
672 & \left(
\begin{array}{cc}
384 & 185472 \\
\end{array}
\right) \\
861 & \left(
\begin{array}{cc}
294 & 144648 \\
\end{array}
\right) \\
1224 & \left(
\begin{array}{cc}
2142 & 5166504 \\
\end{array}
\right) \\
1236 & \left(
\begin{array}{cc}
2163 & 7812756 \\
\end{array}
\right) \\
1248 & \left(
\begin{array}{cc}
2184 & 10509408 \\
\end{array}
\right) \\
1326 & \left(
\begin{array}{cc}
2613 & 8262306 \\
\end{array}
\right) \\
1339 & \left(
\begin{array}{cc}
3193 & 12494209 \\
\end{array}
\right) \\
1344 & \left(
\begin{array}{cc}
2352 & 5955264 \\
\end{array}
\right) \\
1356 & \left(
\begin{array}{cc}
2373 & 8856036 \\
\end{array}
\right) \\
1368 & \left(
\begin{array}{cc}
2394 & 11807208 \\
\end{array}
\right) \\
1428 & \left(
\begin{array}{cc}
2814 & 11768148 \\
\end{array}
\right) \\
1456 & \left(
\begin{array}{cc}
2743 & 9523696 \\
\end{array}
\right) \\
1464 & \left(
\begin{array}{cc}
2562 & 6794424 \\
\end{array}
\right) \\
1476 & \left(
\begin{array}{cc}
2583 & 9949716 \\
\end{array}
\right) \\
1568 & \left(
\begin{array}{cc}
2954 & 13564768 \\
\end{array}
\right) \\
1584 & \left(
\begin{array}{cc}
2772 & 7683984 \\
\end{array}
\right) \\
1586 & \left(
\begin{array}{cc}
2873 & 10865686 \\
\end{array}
\right) \\
1596 & \left(
\begin{array}{cc}
2793 & 11093796 \\
\end{array}
\right) \\
2142 & \left(
\begin{array}{cc}
1224 & 5166504 \\
\end{array}
\right) \\
2163 & \left(
\begin{array}{cc}
1236 & 7812756 \\
\end{array}
\right) \\
2184 & \left(
\begin{array}{cc}
1248 & 10509408 \\
\end{array}
\right) \\
2316 & \left(
\begin{array}{cc}
3504 & 14201712 \\
\end{array}
\right) \\
2328 & \left(
\begin{array}{cc}
4074 & 19164096 \\
\end{array}
\right) \\
2346 & \left(
\begin{array}{cc}
3264 & 15089472 \\
\end{array}
\right) \\
2352 & \left(
\begin{array}{cc}
1344 & 5955264 \\
\end{array}
\right) \\
2369 & \left(
\begin{array}{cc}
3296 & 22818208 \\
\end{array}
\right) \\
2373 & \left(
\begin{array}{cc}
1356 & 8856036 \\
\end{array}
\right) \\
2394 & \left(
\begin{array}{cc}
1368 & 11807208 \\
\end{array}
\right) \\
2412 & \left(
\begin{array}{cc}
1224 & 5166504 \\
\end{array}
\right) \\
2436 & \left(
\begin{array}{cc}
3624 & 15449112 \\
\end{array}
\right) \\
2448 & \left(
\begin{array}{cc}
4284 & 20666016 \\
\end{array}
\right) \\
2532 & \left(
\begin{array}{cc}
1344 & 5955264 \\
\end{array}
\right) \\
2556 & \left(
\begin{array}{cc}
3744 & 16746912 \\
\end{array}
\right) \\
2562 & \left(
\begin{array}{cc}
1464 & 6794424 \\
\end{array}
\right) \\
2568 & \left(
\begin{array}{cc}
4494 & 22218336 \\
\end{array}
\right) \\
2576 & \left(
\begin{array}{cc}
3584 & 17393152 \\
\end{array}
\right) \\
2583 & \left(
\begin{array}{cc}
1476 & 9949716 \\
\end{array}
\right) \\
2613 & \left(
\begin{array}{cc}
1326 & 8262306 \\
\end{array}
\right) \\
2639 & \left(
\begin{array}{cc}
3926 & 24706318 \\
\end{array}
\right) \\
2652 & \left(
\begin{array}{cc}
1464 & 6794424 \\
\end{array}
\right) \\
2676 & \left(
\begin{array}{cc}
3864 & 18095112 \\
\end{array}
\right) \\
2743 & \left(
\begin{array}{cc}
1456 & 9523696 \\
\end{array}
\right) \\
2772 & \left(
\begin{array}{cc}
1584 & 7683984 \\
\end{array}
\right) \\
2793 & \left(
\begin{array}{cc}
1596 & 11093796 \\
\end{array}
\right) \\
2796 & \left(
\begin{array}{cc}
3984 & 19493712 \\
\end{array}
\right) \\
2814 & \left(
\begin{array}{cc}
1428 & 11768148 \\
\end{array}
\right) \\
2873 & \left(
\begin{array}{cc}
1586 & 10865686 \\
\end{array}
\right) \\
2954 & \left(
\begin{array}{cc}
1568 & 13564768 \\
\end{array}
\right) \\
3162 & \left(
\begin{array}{cc}
1326 & 8262306 \\
\end{array}
\right) \\
3193 & \left(
\begin{array}{cc}
1339 & 12494209 \\
\end{array}
\right) \\
3264 & \left(
\begin{array}{cc}
2346 & 15089472 \\
\end{array}
\right) \\
3296 & \left(
\begin{array}{cc}
2369 & 22818208 \\
\end{array}
\right) \\
3468 & \left(
\begin{array}{cc}
4386 & 29973924 \\
\end{array}
\right) \\
3472 & \left(
\begin{array}{cc}
1456 & 9523696 \\
\end{array}
\right) \\
3504 & \left(
\begin{array}{cc}
2316 & 14201712 \\
\end{array}
\right) \\
3528 & \left(
\begin{array}{cc}
4716 & 29116584 \\
\end{array}
\right) \\
3584 & \left(
\begin{array}{cc}
2576 & 17393152 \\
\end{array}
\right) \\
3612 & \left(
\begin{array}{cc}
1236 & 7812756 \\
\end{array}
\right) \\
3624 & \left(
\begin{array}{cc}
2436 & 15449112 \\
\end{array}
\right) \\
3648 & \left(
\begin{array}{cc}
4836 & 30873024 \\
\end{array}
\right) \\
3732 & \left(
\begin{array}{cc}
1356 & 8856036 \\
\end{array}
\right) \\
3744 & \left(
\begin{array}{cc}
2556 & 16746912 \\
\end{array}
\right) \\
3768 & \left(
\begin{array}{cc}
4956 & 32679864 \\
\end{array}
\right) \\
3782 & \left(
\begin{array}{cc}
1586 & 10865686 \\
\end{array}
\right) \\
3852 & \left(
\begin{array}{cc}
1476 & 9949716 \\
\end{array}
\right) \\
3864 & \left(
\begin{array}{cc}
2676 & 18095112 \\
\end{array}
\right) \\
3913 & \left(
\begin{array}{cc}
1339 & 12494209 \\
\end{array}
\right) \\
3926 & \left(
\begin{array}{cc}
2639 & 24706318 \\
\end{array}
\right) \\
3972 & \left(
\begin{array}{cc}
1596 & 11093796 \\
\end{array}
\right) \\
3984 & \left(
\begin{array}{cc}
2796 & 19493712 \\
\end{array}
\right) \\
4053 & \left(
\begin{array}{cc}
2316 & 14201712 \\
\end{array}
\right) \\
4074 & \left(
\begin{array}{cc}
2328 & 19164096 \\
\end{array}
\right) \\
4182 & \left(
\begin{array}{cc}
1428 & 11768148 \\
\end{array}
\right) \\
4221 & \left(
\begin{array}{cc}
2142 & 5166504 \\
\end{array}
\right) \\
4263 & \left(
\begin{array}{cc}
2436 & 15449112 \\
\end{array}
\right) \\
4284 & \left(
\begin{array}{cc}
2448 & 20666016 \\
\end{array}
\right) \\
4386 & \left(
\begin{array}{cc}
3468 & 29973924 \\
\end{array}
\right) \\
4431 & \left(
\begin{array}{cc}
2352 & 5955264 \\
\end{array}
\right) \\
4439 & \left(
\begin{array}{cc}
6176 & 41478016 \\
\end{array}
\right) \\
4473 & \left(
\begin{array}{cc}
2556 & 16746912 \\
\end{array}
\right) \\
4494 & \left(
\begin{array}{cc}
2568 & 22218336 \\
\end{array}
\right) \\
4592 & \left(
\begin{array}{cc}
1568 & 13564768 \\
\end{array}
\right) \\
4623 & \left(
\begin{array}{cc}
2346 & 15089472 \\
\end{array}
\right) \\
4641 & \left(
\begin{array}{cc}
2562 & 6794424 \\
\end{array}
\right) \\
4669 & \left(
\begin{array}{cc}
6496 & 45121216 \\
\end{array}
\right) \\
4683 & \left(
\begin{array}{cc}
2676 & 18095112 \\
\end{array}
\right) \\
4704 & \left(
\begin{array}{cc}
2328 & 19164096 \\
\end{array}
\right) \\
4716 & \left(
\begin{array}{cc}
3528 & 29116584 \\
\end{array}
\right) \\
4812 & \left(
\begin{array}{cc}
1248 & 10509408 \\
\end{array}
\right) \\
4824 & \left(
\begin{array}{cc}
2448 & 20666016 \\
\end{array}
\right) \\
4836 & \left(
\begin{array}{cc}
3648 & 30873024 \\
\end{array}
\right) \\
4851 & \left(
\begin{array}{cc}
2772 & 7683984 \\
\end{array}
\right) \\
4853 & \left(
\begin{array}{cc}
2576 & 17393152 \\
\end{array}
\right) \\
4893 & \left(
\begin{array}{cc}
2796 & 19493712 \\
\end{array}
\right) \\
4932 & \left(
\begin{array}{cc}
1368 & 11807208 \\
\end{array}
\right) \\
4944 & \left(
\begin{array}{cc}
2568 & 22218336 \\
\end{array}
\right) \\
4956 & \left(
\begin{array}{cc}
3768 & 32679864 \\
\end{array}
\right) \\
6132 & \left(
\begin{array}{cc}
3504 & 14201712 \\
\end{array}
\right) \\
6174 & \left(
\begin{array}{cc}
3528 & 29116584 \\
\end{array}
\right) \\
6176 & \left(
\begin{array}{cc}
4439 & 41478016 \\
\end{array}
\right) \\
6231 & \left(
\begin{array}{cc}
2613 & 8262306 \\
\end{array}
\right) \\
6293 & \left(
\begin{array}{cc}
2639 & 24706318 \\
\end{array}
\right) \\
6321 & \left(
\begin{array}{cc}
2163 & 7812756 \\
\end{array}
\right) \\
6342 & \left(
\begin{array}{cc}
3624 & 15449112 \\
\end{array}
\right) \\
6384 & \left(
\begin{array}{cc}
3648 & 30873024 \\
\end{array}
\right) \\
6432 & \left(
\begin{array}{cc}
3264 & 15089472 \\
\end{array}
\right) \\
6496 & \left(
\begin{array}{cc}
4669 & 45121216 \\
\end{array}
\right) \\
6531 & \left(
\begin{array}{cc}
2373 & 8856036 \\
\end{array}
\right) \\
6541 & \left(
\begin{array}{cc}
2743 & 9523696 \\
\end{array}
\right) \\
6552 & \left(
\begin{array}{cc}
3744 & 16746912 \\
\end{array}
\right) \\
6594 & \left(
\begin{array}{cc}
3768 & 32679864 \\
\end{array}
\right) \\
6600 & \left(
\begin{array}{cc}
528 & 435600 \\
\end{array}
\right) \\
6716 & \left(
\begin{array}{cc}
4439 & 41478016 \\
\end{array}
\right) \\
6741 & \left(
\begin{array}{cc}
2583 & 9949716 \\
\end{array}
\right) \\
6752 & \left(
\begin{array}{cc}
3584 & 17393152 \\
\end{array}
\right) \\
6762 & \left(
\begin{array}{cc}
3864 & 18095112 \\
\end{array}
\right) \\
6834 & \left(
\begin{array}{cc}
3468 & 29973924 \\
\end{array}
\right) \\
6851 & \left(
\begin{array}{cc}
2873 & 10865686 \\
\end{array}
\right) \\
6923 & \left(
\begin{array}{cc}
2369 & 22818208 \\
\end{array}
\right) \\
6946 & \left(
\begin{array}{cc}
4669 & 45121216 \\
\end{array}
\right) \\
6951 & \left(
\begin{array}{cc}
2793 & 11093796 \\
\end{array}
\right) \\
6972 & \left(
\begin{array}{cc}
3984 & 19493712 \\
\end{array}
\right) \\
8232 & \left(
\begin{array}{cc}
4074 & 19164096 \\
\end{array}
\right) \\
8241 & \left(
\begin{array}{cc}
2814 & 11768148 \\
\end{array}
\right) \\
8253 & \left(
\begin{array}{cc}
4716 & 29116584 \\
\end{array}
\right) \\
8421 & \left(
\begin{array}{cc}
2184 & 10509408 \\
\end{array}
\right) \\
8442 & \left(
\begin{array}{cc}
4284 & 20666016 \\
\end{array}
\right) \\
8463 & \left(
\begin{array}{cc}
4836 & 30873024 \\
\end{array}
\right) \\
8631 & \left(
\begin{array}{cc}
2394 & 11807208 \\
\end{array}
\right) \\
8643 & \left(
\begin{array}{cc}
4386 & 29973924 \\
\end{array}
\right) \\
8651 & \left(
\begin{array}{cc}
2954 & 13564768 \\
\end{array}
\right) \\
8652 & \left(
\begin{array}{cc}
4494 & 22218336 \\
\end{array}
\right) \\
8673 & \left(
\begin{array}{cc}
4956 & 32679864 \\
\end{array}
\right) \\
9331 & \left(
\begin{array}{cc}
3193 & 12494209 \\
\end{array}
\right) \\
9344 & \left(
\begin{array}{cc}
6176 & 41478016 \\
\end{array}
\right) \\
9362 & \left(
\begin{array}{cc}
3926 & 24706318 \\
\end{array}
\right) \\
9632 & \left(
\begin{array}{cc}
3296 & 22818208 \\
\end{array}
\right) \\
9664 & \left(
\begin{array}{cc}
6496 & 45121216 \\
\end{array}
\right) \\
\end{array}\]

nyy

nyy 发表于 2025-2-24 10:09
输出结果
{144, 156, 168, 252, 273, 276, 294, 372, 384, 441, 483, 492, 651, \
672, 861, 1224, 1236, ...

再加两句

1. ccc=Select[Flatten[#]&/@bbb,#[[1]]<=#[[2]]&]
   
2. Grid[ccc,Alignment->Left](*列表显示*)
   

复制代码

输出结果
{{144, 252, 63504}, {156, 273, 101556}, {168, 294, 144648}, {276, 384,
   185472}, {1224, 2142, 5166504}, {1236, 2163, 7812756}, {1248, 2184,
   10509408}, {1326, 2613, 8262306}, {1339, 3193, 12494209}, {1344,
  2352, 5955264}, {1356, 2373, 8856036}, {1368, 2394,
  11807208}, {1428, 2814, 11768148}, {1456, 2743, 9523696}, {1464,
  2562, 6794424}, {1476, 2583, 9949716}, {1568, 2954,
  13564768}, {1584, 2772, 7683984}, {1586, 2873, 10865686}, {1596,
  2793, 11093796}, {2316, 3504, 14201712}, {2328, 4074,
  19164096}, {2346, 3264, 15089472}, {2369, 3296, 22818208}, {2436,
  3624, 15449112}, {2448, 4284, 20666016}, {2556, 3744,
  16746912}, {2568, 4494, 22218336}, {2576, 3584, 17393152}, {2639,
  3926, 24706318}, {2676, 3864, 18095112}, {2796, 3984,
  19493712}, {3468, 4386, 29973924}, {3528, 4716, 29116584}, {3648,
  4836, 30873024}, {3768, 4956, 32679864}, {4439, 6176,
  41478016}, {4669, 6496, 45121216}}

列表结果
\[\begin{array}{lll}
144 & 252 & 63504 \\
156 & 273 & 101556 \\
168 & 294 & 144648 \\
276 & 384 & 185472 \\
1224 & 2142 & 5166504 \\
1236 & 2163 & 7812756 \\
1248 & 2184 & 10509408 \\
1326 & 2613 & 8262306 \\
1339 & 3193 & 12494209 \\
1344 & 2352 & 5955264 \\
1356 & 2373 & 8856036 \\
1368 & 2394 & 11807208 \\
1428 & 2814 & 11768148 \\
1456 & 2743 & 9523696 \\
1464 & 2562 & 6794424 \\
1476 & 2583 & 9949716 \\
1568 & 2954 & 13564768 \\
1584 & 2772 & 7683984 \\
1586 & 2873 & 10865686 \\
1596 & 2793 & 11093796 \\
2316 & 3504 & 14201712 \\
2328 & 4074 & 19164096 \\
2346 & 3264 & 15089472 \\
2369 & 3296 & 22818208 \\
2436 & 3624 & 15449112 \\
2448 & 4284 & 20666016 \\
2556 & 3744 & 16746912 \\
2568 & 4494 & 22218336 \\
2576 & 3584 & 17393152 \\
2639 & 3926 & 24706318 \\
2676 & 3864 & 18095112 \\
2796 & 3984 & 19493712 \\
3468 & 4386 & 29973924 \\
3528 & 4716 & 29116584 \\
3648 & 4836 & 30873024 \\
3768 & 4956 & 32679864 \\
4439 & 6176 & 41478016 \\
4669 & 6496 & 45121216 \\
\end{array}\]