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

1,8

Comments

Every term divides all its successors.

Links

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

Formula

a(n) = n!/A248769(n).

Example

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

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 *)

Crossrefs

Cf. A248768, A248769, A000142.

Sequence in context: A330574 A126271 A010871 * A022366 A165853 A035037

Adjacent sequences: A248764 A248765 A248766 * A248768 A248769 A248770

Keyword

nonn,easy

Author

Clark Kimberling, Oct 14 2014

Status

approved