一百单八将的由来

王守恩

northwolves 发表于 2024-4-30 19:55
{535537,10,{{3025,532512},{4096,531441},{93312,442225},{172225,363312},{194481,341056},{341056,1 ...

把疑惑一并提出来。
{1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 72, 81, 100, 108, 121, 125, 128, 144, 169, 196, 200, 216, 225, 243, 256, 288, 289, 324, 343, 361, 392, 400, 432, 441, 484, 500, 512, 529, 576,
625, 648, 675, 676, 729, 784, 800, 841, 864, 900, 961, 968, 972, 1000, 1024, 1089, 1125, 1152, 1156, 1225, 1296, 1323, 1331, 1352, 1369, 1372, 1444, 1521, 1568, 1600, 1681, 1728,
1764, 1800, 1849, 1936, 1944, 2000, 2025, 2048, 2116, 2187, 2197, 2209, 2304, 2312, 2401, 2500, 2592, 2601, 2700, 2704, 2744, 2809, 2888, 2916, 3025, 3087, 3125, 3136, 3200, ......

在上面这串数中, 随意取3个(可以重复)相加。

a(1)=0,
a(2)=0,  
a(3)=1,  1+1+1,
a(4)=0,
a(5)=0,  
a(6)=1,  1+1+4,
a(7)=0,
a(8)=0,  
a(9)=1,  1+4+4,
a(10)=1, 1+1+8,
a(11)=1, 1+1+9
a(12)=1, 4+4+4,
a(13)=1, 1+4+8,
a(14)=1,1+4+9,
a(15)=0,
a(16)=1, 4+4+8,
a(17)=2, 1+8+8=4+4+9,
a(18)=2, 1+1+16=1+8+9,
a(19)=1, 1+9+9,
......
得到这样一串数。OEIS好像没有这串数？
{0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 1, 1, 2, 1, 0, 2, 2, 2, 2, 1, 2, 1, 0, 2, 3, 3, 2, 2, 3, 2, 1, 3, 4, 3, 2, 4, 4, 1, 1, 3, 4, 2, 3, 3, 3, 3, 1, 3, 3, 4, 3,
3, 4, 3, 2, 2, 4, 5, 3, 4, 4, 2, 1, 4, 5, 3, 3, 3, 6, 1, 2, 5, 6, 5, 2, 5, 3, 4, 0, 4, 7, 6, 2, 3, 4, 2, 2, 3, 6, 4, 5, 4, 5, 2, 2, 4, 6, 4, 4, 6, 4, 4, 0, 6, 6, 5, 2, 6, 8,
4, 0, 3, 6, 5, 2, 5, 7, 4, 1, 3, 6, 2, 4, 4, 6, 4, 3, 6, 5, 3, 2, 7, 4, 2, 2, 7, 6, 3, 1, 5, 5, 2, 1, 5, 7, 3, 2, 1, 5, 3, 1, 4, 5, 4, 3, 2, 4, 3, 1, 3, 3, 3, 3, 5, 4, ....

1. Select[Range[360], # == 1 || Min[FactorInteger[#][[;; , 2]]] > 1 &]; BinCounts[Select[Plus @@@ Union[Sort /@ Tuples[pow, {3}]], # <= 360 &]]

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相加的和不会={1, 2, 4, 5, 7, 8, 15, 23, 31, 87, 111, 119,  就这12个}？公式也不对！