A248773 Greatest 7th power integer that divides n!.

1, 1, 1, 1, 1, 1, 1, 128, 128, 128, 128, 128, 128, 128, 128, 16384, 16384, 35831808, 35831808, 35831808, 35831808, 35831808, 35831808, 4586471424, 4586471424, 4586471424, 4586471424, 4586471424, 4586471424, 783641640960000000, 783641640960000000

Offset: 1

Author

Clark Kimberling, Oct 14 2014

Keywords

• nonn
• easy

Comments

Every term divides all its successors.

Examples

			a(8) = 128 because 128 divides 8! and if k > 2 then k^7 does not divide 8!.
		

Links

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

Crossrefs

Cf. A248774, A248775, 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 = 7; Table[p[m, n], {n, 1, z}]  (* A248773 *)
Table[p[m, n]^(1/m), {n, 1, z}]   (* A248774 *)
Table[n!/p[m, n], {n, 1, z}]      (* A248775 *)

Formula

a(n) = n!/A248775(n).