A248770 Greatest 6th power integer that divides n!.

1, 1, 1, 1, 1, 1, 1, 64, 64, 64, 64, 64, 64, 64, 46656, 2985984, 2985984, 2985984, 2985984, 191102976, 191102976, 191102976, 191102976, 191102976, 2985984000000, 2985984000000, 2176782336000000, 139314069504000000, 139314069504000000, 139314069504000000

Offset: 1

Author

Clark Kimberling, Oct 14 2014

Keywords

• nonn
• easy

Comments

Every term divides all its successors.

Examples

			a(8) = 64 because 64 divides 8! and if k > 2 then k^6 does not divide 8!.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A248771, A248772, A000142.

Programs

Mathematica

z = 50; 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 = 6; Table[p[m, n], {n, 1, z}]  (* A248770 *)
Table[p[m, n]^(1/m), {n, 1, z}]   (* A248771 *)
Table[n!/p[m, n], {n, 1, z}]      (* A248772 *)

Formula

a(n) = n!/A248772(n).