A248773 Greatest 7th power integer that divides n!.

1, 1, 1, 1, 1, 1, 1, 128, 128, 128, 128, 128, 128, 128, 128, 16384, 16384, 35831808, 35831808, 35831808, 35831808, 35831808, 35831808, 4586471424, 4586471424, 4586471424, 4586471424, 4586471424, 4586471424, 783641640960000000, 783641640960000000

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!/A248775(n).

Example

a(8) = 128 because 128 divides 8! and if k > 2 then k^7 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 = 7; Table[p[m, n], {n, 1, z}]  (* A248773 *)
Table[p[m, n]^(1/m), {n, 1, z}]   (* A248774 *)
Table[n!/p[m, n], {n, 1, z}]      (* A248775 *)

Crossrefs

Cf. A248774, A248775, A000142.

Sequence in context: A172532 A173779 A187353 * A217847 A223591 A097758

Adjacent sequences: A248770 A248771 A248772 * A248774 A248775 A248776

Keyword

nonn,easy

Author

Clark Kimberling, Oct 14 2014

Status

approved