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A248782 Number of integers k^5 that divide n!.

%I A248782 #8 Oct 27 2014 20:48:00
%S A248782 1,1,1,1,1,1,1,2,2,2,2,6,6,6,6,8,8,8,8,8,8,8,8,15,30,30,30,36,36,36,
%T A248782 36,42,56,56,112,112,112,128,128,128,128,128,128,144,270,270,270,300,
%U A248782 300,300,300,300,300,396,792,792,792,792,792,864,864,864,1512
%N A248782 Number of integers k^5 that divide n!.
%H A248782 Clark Kimberling, <a href="/A248782/b248782.txt">Table of n, a(n) for n = 1..1000</a>
%e A248782 a(12) counts these divisors of 12!:  1, 32, 243, 1024, 7776, 248832.
%t A248782 z = 130; m = 5;
%t A248782 f[n_] := f[n] = FactorInteger[n!]; r[x_] := r[x] = m*Floor[x/m]
%t A248782 u[n_] := Table[f[n][[i, 1]], {i, 1, Length[f[n]]}];
%t A248782 v[n_] := Table[f[n][[i, 2]], {i, 1, Length[f[n]]}];
%t A248782 a[n_] := Apply[Times, 1 + r[v[n]]/m]
%t A248782 t = Table[a[n], {n, 1, z}] (* A248782 *)
%o A248782 (PARI) a(n)=c=0;d=divisors(n!);for(i=1,#d,if(ispower(d[i])&&ispower(d[i])%5==0,c++));c+1
%o A248782 n=1;while(n<50,print1(a(n),", ");n++) \\ _Derek Orr_, Oct 20 2014
%Y A248782 Cf. A000142, A055993, A248780, A248781, A248768.
%K A248782 nonn,easy
%O A248782 1,8
%A A248782 _Clark Kimberling_, Oct 15 2014