A248769 Greatest 5th-power-free divisor of n!.

1, 2, 6, 24, 120, 720, 5040, 1260, 11340, 113400, 1247400, 1925, 25025, 350350, 5255250, 2627625, 44669625, 804053250, 15277011750, 305540235000, 6416344935000, 141159588570000, 3246670537110000, 10020588077500, 80164704620, 2084282320120, 56275622643240

Offset: 1

Author

Clark Kimberling, Oct 14 2014

Keywords

• nonn
• easy

Examples

			a(8) = 1260 because 1260 divides 8! and if k > 1260 divides 8!, then h^5 divides 8!/k for some h > 1.
		

Links

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

Crossrefs

Cf. A248767, A248768, 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 = 5; Table[p[m, n], {n, 1, z}]  (* A248767 *)
Table[p[m, n]^(1/m), {n, 1, z}]   (* A248768 *)
Table[n!/p[m, n], {n, 1, z}]      (* A248769 *)

Formula

a(n) = n!/A248767(n).