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A248782
Number of integers k^5 that divide n!.
2
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, 36, 42, 56, 56, 112, 112, 112, 128, 128, 128, 128, 128, 128, 144, 270, 270, 270, 300, 300, 300, 300, 300, 300, 396, 792, 792, 792, 792, 792, 864, 864, 864, 1512
OFFSET
1,8
LINKS
EXAMPLE
a(12) counts these divisors of 12!: 1, 32, 243, 1024, 7776, 248832.
MATHEMATICA
z = 130; m = 5;
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}] (* A248782 *)
PROG
(PARI) a(n)=c=0; d=divisors(n!); for(i=1, #d, if(ispower(d[i])&&ispower(d[i])%5==0, c++)); c+1
n=1; while(n<50, print1(a(n), ", "); n++) \\ Derek Orr, Oct 20 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 15 2014
STATUS
approved