OFFSET
1,2
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..1000
FORMULA
a(n) = n!/A248773(n).
EXAMPLE
a(8) = 315 because 315 divides 8! and if k > 315 divides 8!, then h^7 divides 8!/k for some h > 1.
MATHEMATICA
z = 60; f[n_] := f[n] = FactorInteger[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]]}];
p[m_, n_] := p[m, n] = Product[u[n][[i]]^r[m, v[n]][[i]], {i, 1, Length[f[n]]}];
m = 8; Table[p[m, n], {n, 1, z}] (* A248776 *)
Table[p[m, n]^(1/m), {n, 1, z}] (* A248777 *)
Table[n!/p[m, n], {n, 1, z}] (* A248778 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 14 2014
STATUS
approved