OFFSET
1,5
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..1000 (first 400 terms from Clark Kimberling)
EXAMPLE
a(7) counts these integers k^6 that divide 125411328000 = A000178(6): 1, 64, 729, 4096, 46656, 2985984, these being k^6 for k = 1, 2, 3, 4, 6, 12.
MAPLE
b:= proc(n) option remember; add(i[2]*x^numtheory[pi](i[1]),
i=ifactors(n)[2])+`if`(n=1, 0, b(n-1))
end:
c:= proc(n) option remember; b(n)+`if`(n=1, 0, c(n-1)) end:
a:= n->(p->mul(iquo(coeff(p, x, i), 6)+1, i=1..degree(p)))(c(n)):
seq(a(n), n=1..30); # Alois P. Heinz, Oct 16 2014
MATHEMATICA
z = 40; p[n_] := Product[k!, {k, 1, n}];
f[n_] := f[n] = FactorInteger[p[n]];
r[m_, x_] := r[m, 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]]}];
t[m_, n_] := Apply[Times, 1 + r[m, v[n]]/m]
m = 6; Table[t[m, n], {n, 1, z}] (* A248824 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 15 2014
STATUS
approved