A248776 Greatest 8th power integer that divides n!

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

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