A248772 Greatest 6th-power-free divisor of n!.

1, 2, 6, 24, 120, 720, 5040, 630, 5670, 56700, 623700, 7484400, 97297200, 1362160800, 28028000, 7007000, 119119000, 2144142000, 40738698000, 12730843125, 267347705625, 5881649523750, 135277939046250, 3246670537110000, 5194672859376, 135061494343776

Offset: 1

Author

Clark Kimberling, Oct 14 2014

Keywords

• nonn
• easy

Examples

			a(8) = 630 because 630 divides 8! and if k > 630 divides 8!, then h^6 divides 8!/k for some h > 1.
		

Links

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

Crossrefs

Cf. A248770, A248771, 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!/A248770(n).