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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

Clark Kimberling and Alois P. Heinz, Table of n, a(n) for n = 1..1000 (first 400 terms from Clark Kimberling)

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)):

seq(a(n), n=1..30);  # Alois P. Heinz, Oct 16 2014

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

Cf. A000178, A000578, A248784, A248822, A248823.

Sequence in context: A233896 A118039 A218965 * A260559 A258079 A027165

Adjacent sequences:  A248818 A248819 A248820 * A248822 A248823 A248824

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Oct 15 2014

STATUS

approved

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Last modified March 26 06:48 EDT 2019. Contains 321481 sequences. (Running on oeis4.)