OFFSET
1,4
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..1000
FORMULA
a(n) = product_{i=1..r} 1+floor(e[i]/3), where product_{i=1..r} p[i]^e[i] is the prime factorization of n!. - M. F. Hasler, Oct 22 2014
EXAMPLE
a(9) counts these divisors of 9!: 1, 8, 27, 64, 216, 1728.
MATHEMATICA
z = 130; m = 3; f[n_] := f[n] = FactorInteger[n!];
v[n_] := Table[f[n][[i, 2]], {i, 1, Length[f[n]]}];
a[n_] := Apply[Times, 1 + Floor[v[n]/m]]
A248780 = Table[a[n], {n, 1, z}] (* simplified by M. F. Hasler, Oct 22 2014 *)
PROG
(PARI) a(n)=sumdiv(n!, d, ispower(d, 3))
for(n=1, 50, print1(a(n), ", ")) \\ Derek Orr, Oct 20 2014, simplified by M. F. Hasler, Oct 22 2014
(PARI) A248780(n)=prod(i=1, #n=factor(n!)[, 2], 1+n[i]\3) \\ M. F. Hasler, Oct 22 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 15 2014
STATUS
approved