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A248776 Greatest 8th power integer that divides n! 3
1, 1, 1, 1, 1, 1, 1, 1, 1, 256, 256, 256, 256, 256, 256, 256, 256, 429981696, 429981696, 429981696, 429981696, 429981696, 429981696, 429981696, 429981696, 429981696, 429981696, 110075314176, 110075314176, 110075314176, 110075314176, 110075314176 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,10

COMMENTS

Every term divides all its successors.

LINKS

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

FORMULA

a(n) = n!/A248778(n).

EXAMPLE

a(8) = 128 because 128 divides 8! and if k > 2 then k^8 does not divide 8!.

MATHEMATICA

z = 60; 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 = 8; Table[p[m, n], {n, 1, z}] (* A248776 *)

Table[p[m, n]^(1/m), {n, 1, z}] (* A248777 *)

Table[n!/p[m, n], {n, 1, z}] (* A248778 *)

Module[{e=Range[30]^8}, Table[Max[Select[e, Divisible[n!, #]&]], {n, 40}]] (* Harvey P. Dale, Dec 23 2019 *)

CROSSREFS

Cf. A248777, A248778, A000142.

Sequence in context: A186482 A186474 A093861 * A223600 A217848 A044872

Adjacent sequences: A248773 A248774 A248775 * A248777 A248778 A248779

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Oct 14 2014

STATUS

approved

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Last modified February 8 23:03 EST 2023. Contains 360153 sequences. (Running on oeis4.)