A248781 Number of integers k^4 that divide n!

1, 1, 1, 1, 1, 2, 2, 2, 4, 6, 6, 6, 6, 6, 6, 8, 8, 15, 15, 30, 30, 30, 30, 36, 36, 36, 48, 112, 112, 112, 112, 128, 128, 144, 216, 270, 270, 270, 270, 300, 300, 300, 300, 660, 792, 792, 792, 864, 1296, 1728, 1728, 3744, 3744, 4368, 4368, 4704, 4704, 4704

Offset

1,6

Links

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

Example

a(10) counts these divisors of 10!:  1, 16, 81, 256, 1296, 20736.

Mathematica

z = 130; m = 4;
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}] (* A248781 *)

Prog

(PARI) a(n)=c=0; d=divisors(n!); for(i=1, #d, if(ispower(d[i])&&ispower(d[i])%4==0, c++)); c+1
n=1; while(n<50, print1(a(n), ", "); n++) \\ Derek Orr, Oct 20 2014

Crossrefs

Cf. A000142, A055993, A248780, A248765.

Sequence in context: A320908 A356692 A361404 * A236840 A378992 A182539

Adjacent sequences: A248778 A248779 A248780 * A248782 A248783 A248784

Keyword

nonn,easy

Author

Clark Kimberling, Oct 15 2014

Status

approved