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

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]]}];
a[n_] := Apply[Times, 1 + r[v[n]]/m]
t = Table[a[n], {n, 1, z}] (* A248783 *)

Prog

(PARI) a(n)=c=0; d=divisors(n!); for(i=1, #d, if(ispower(d[i])&&ispower(d[i])%6==0, c++)); c+1
n=1; while(n<50, print1(a(n), ", "); n++) \\ Derek Orr, Oct 20 2014

Crossrefs

Cf. A000142, A055993, A248780, A248781, A248782, A248771.

Sequence in context: A105267 A280263 A008838 * A244462 A063790 A334510

Adjacent sequences: A248780 A248781 A248782 * A248784 A248785 A248786

Keyword

nonn,easy

Author

Clark Kimberling, Oct 15 2014

Status

approved