A248767 Greatest 5th power integer that divides n!.

1, 1, 1, 1, 1, 1, 1, 32, 32, 32, 32, 248832, 248832, 248832, 248832, 7962624, 7962624, 7962624, 7962624, 7962624, 7962624, 7962624, 7962624, 61917364224, 193491763200000, 193491763200000, 193491763200000, 6191736422400000, 6191736422400000, 6191736422400000

Offset: 1

Author

Clark Kimberling, Oct 14 2014

Keywords

• nonn
• easy

Comments

Every term divides all its successors.

Examples

			a(8) = 32 because 32 divides 8! and if k > 2 then k^5 does not divide 8!.
		

Links

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

Crossrefs

Cf. A248768, A248769, 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!/A248769(n).