将3,4,5,6,…,n排成数列{a(k):k=1,2,3,4,5,…,n-2},使a(k)都是k的倍数,有几种排法?
a(01)=b(03)=1,{3},
a(02)=b(03)*b(04)=1,{3,4},
a(03)=b(04)*b(05)=1,{5,4,3},
a(04)=b(05)*b(06)=1,{5,6,3,4},
a(05)=b(06)*b(07)=1,{7,6,3,4,5},
a(06)=b(07)*b(08)=2,{7,4,3,8,5,6},{7,8,3,4,5,6},
a(07)=b(08)*b(09)=4,{3,4,8,9,5,6,7},{3,8,9,4,5,6,7},{9,4,3,8,5,6,7}{9,8,3,4,5,6,7},
a(08)=b(09)*b(10)=2,{3,10,9,4,5,6,7,8},{9,10,3,4,5,6,7,8},
a(09)=b(10)*b(11)=1,{11,10,3,4,5,6,7,8,9},
a(10)=b(11)*b(12)=3,{11,4,3,12,5,6,7,8,9,10},{11,6,3,4,5,12,7,8,9,10},{11,12,3,4,5,6,7,8,9,10},
a(11)=b(12)*b(13)=3,{13,4,3,12,5,6,7,8,9,10,11},{13,6,3,4,5,12,7,8,9,10,11},{13,12,3,4,5,6,7,8,9,10,11},
a(12)=b(13)*b(14)=1,{13,14,3,4,5,6,7,8,9,10,11,12},
a(13)=b(14)*b(15)=3,
得到这样一串数:1,1,1,1,1,1,2,4,2,1,3,3,1,3,12,4,2,2,3,9,3,1,8,16,2,4,12,3,3,3,8,24,...
把这串数分成A,B,
A=1,1,1,2,2,3,1,12,2,3,3,08,2,12,3,08,...
B=1,1,1,4,1,3,3,04,2,9,1,16,4,03,3,24,...
- A:Table[b[n_] := If[n < 2, 1, b /@ Most@Divisors[n] // Total]; s = {b[k], b[2 k - 1]}; {s, Times @@ s}, {k, 1, 19}]
复制代码
{{{1, 1}, 1}, {{1, 1}, 1}, {{1, 1}, 1}, {{2, 1}, 2}, {{1, 2}, 2}, {{3, 1}, 3}, {{1, 1}, 1}, {{4, 3}, 12}, {{2, 1}, 2}, {{3, 1}, 3}, {{1, 3}, 3}, {{8, 1}, 08}, {{1, 2}, 2}, {{3, 4}, 12}, {{3, 1}, 3}, {{8, 1}, 08}, {{1, 3}, 3}, {{8, 3}, 24}, {{1, 1}, 1}}
- B:Table[b[n_] := If[n < 2, 1, b /@ Most@Divisors[n] // Total]; s = {b[k], b[2 k + 1]}; {s, Times @@ s}, {k, 1, 19}]
复制代码
{{{1, 1}, 1}, {{1, 1}, 1}, {{1, 1}, 1}, {{2, 2}, 4}, {{1, 1}, 1}, {{3, 1}, 3}, {{1, 3}, 3}, {{4, 1}, 04}, {{2, 1}, 2}, {{3, 3}, 9}, {{1, 1}, 1}, {{8, 2}, 16}, {{1, 4}, 4}, {{3, 1}, 03}, {{3, 1}, 3}, {{8, 3}, 24}, {{1, 3}, 3}, {{8, 1}, 08}, {{1, 3}, 3}}
A,B可以化简吗?A,B可以合并吗?A,B合并后可以只出现1,1,1,1,1,1,2,4,2,1,3,3,1,3,12,4,2,2,3,9,3,1,8,16,2,4,12,3,3,3,8,24,...?谢谢各位! |