|
|
A248821
|
|
Number of cubes that divide 1!*2!*3!*...*n!.
|
|
5
|
|
|
1, 1, 1, 2, 6, 10, 36, 64, 220, 468, 1024, 2052, 7590, 16224, 50400, 142800, 246240, 510300, 2261952, 3545856, 14152320, 40986000, 68428800, 178293960, 784274400, 1526805504, 2782080000, 9307872000, 15858633600, 28225260000, 143730892800, 225167040000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,4
|
|
LINKS
|
|
|
EXAMPLE
|
a(5) counts these cubes that divide 34560: 1^3, 2^3, 3^3, 4^3, 6^3, 12^3.
|
|
MAPLE
|
b:= proc(n) option remember; add(i[2]*x^numtheory[pi](i[1]),
i=ifactors(n)[2])+`if`(n=1, 0, b(n-1))
end:
c:= proc(n) option remember; b(n)+`if`(n=1, 0, c(n-1)) end:
a:= n->(p->mul(iquo(coeff(p, x, i), 3)+1, i=1..degree(p)))(c(n)):
|
|
MATHEMATICA
|
z = 40; p[n_] := Product[k!, {k, 1, n}];
f[n_] := f[n] = FactorInteger[p[n]];
r[m_, x_] := r[m, x] = m*Floor[x/m]
u[n_] := Table[f[n][[i, 1]], {i, 1, Length[f[n]]}];
v[n_] := Table[f[n][[i, 2]], {i, 1, Length[f[n]]}];
t[m_, n_] := Apply[Times, 1 + r[m, v[n]]/m]
m = 3; Table[t[m, n], {n, 1, z}] (* A248821 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|