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A248768 Greatest k such that k^5 divides n! 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 22 09:51 EDT 2021. Contains 348160 sequences. (Running on oeis4.)