cp's OEIS Frontend

A248781 Number of integers k^4 that divide n!

%I A248781 #6 Oct 26 2014 21:08:34
%S A248781 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,
%T A248781 112,112,112,128,128,144,216,270,270,270,270,300,300,300,300,660,792,
%U A248781 792,792,864,1296,1728,1728,3744,3744,4368,4368,4704,4704,4704
%N A248781 Number of integers k^4 that divide n!
%H A248781 Clark Kimberling, <a href="/A248781/b248781.txt">Table of n, a(n) for n = 1..1000</a>
%e A248781 a(10) counts these divisors of 10!:  1, 16, 81, 256, 1296, 20736.
%t A248781 z = 130; m = 4;
%t A248781 f[n_] := f[n] = FactorInteger[n!]; r[x_] := r[x] = m*Floor[x/m]
%t A248781 u[n_] := Table[f[n][[i, 1]], {i, 1, Length[f[n]]}];
%t A248781 v[n_] := Table[f[n][[i, 2]], {i, 1, Length[f[n]]}];
%t A248781 a[n_] := Apply[Times, 1 + r[v[n]]/m]
%t A248781 t = Table[a[n], {n, 1, z}] (* A248781 *)
%o A248781 (PARI) a(n)=c=0;d=divisors(n!);for(i=1,#d,if(ispower(d[i])&&ispower(d[i])%4==0,c++));c+1
%o A248781 n=1;while(n<50,print1(a(n),", ");n++) \\ _Derek Orr_, Oct 20 2014
%Y A248781 Cf. A000142, A055993, A248780, A248765.
%K A248781 nonn,easy
%O A248781 1,6
%A A248781 _Clark Kimberling_, Oct 15 2014