A248768 Greatest k such that k^5 divides n!

1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 12, 12, 12, 12, 24, 24, 24, 24, 24, 24, 24, 24, 144, 720, 720, 720, 1440, 1440, 1440, 1440, 2880, 8640, 8640, 60480, 60480, 60480, 120960, 120960, 120960, 120960, 120960, 120960, 241920, 3628800, 3628800, 3628800, 7257600

Offset

1,8

Comments

Every term divides all its successors.

Links

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

Example

a(8) = 2 because 2^5 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. A248767, A248769, A000142.

Sequence in context: A316497 A084961 A226398 * A334509 A029643 A100687

Adjacent sequences: A248765 A248766 A248767 * A248769 A248770 A248771

Keyword

nonn,easy

Author

Clark Kimberling, Oct 14 2014

Status

approved