A248783 - OEIS

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A248783

Number of integers k^6 that divide n!.

1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 4, 6, 6, 6, 6, 8, 8, 8, 8, 8, 16, 16, 24, 30, 30, 30, 30, 36, 36, 36, 36, 36, 36, 36, 48, 56, 56, 112, 112, 112, 112, 128, 128, 128, 128, 192, 192, 216, 216, 270, 270, 270, 270, 300, 300, 300, 300, 300, 360, 396, 396

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OFFSET

1,8

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..1000

EXAMPLE

a(16) counts these divisors of 16!: 1^6, 2^6, 2^12, 3^6, 6^6, 12^6.

MATHEMATICA

z = 130; m = 6;

f[n_] := f[n] = FactorInteger[n!]; r[x_] := r[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]]}];