A248770 Greatest 6th power integer that divides n!.

1, 1, 1, 1, 1, 1, 1, 64, 64, 64, 64, 64, 64, 64, 46656, 2985984, 2985984, 2985984, 2985984, 191102976, 191102976, 191102976, 191102976, 191102976, 2985984000000, 2985984000000, 2176782336000000, 139314069504000000, 139314069504000000, 139314069504000000

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!/A248772(n).

Example

a(8) = 64 because 64 divides 8! and if k > 2 then k^6 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 = 6; Table[p[m, n], {n, 1, z}]  (* A248770 *)
Table[p[m, n]^(1/m), {n, 1, z}]   (* A248771 *)
Table[n!/p[m, n], {n, 1, z}]      (* A248772 *)

Crossrefs

Cf. A248771, A248772, A000142.

Sequence in context: A188828 A331224 A123994 * A272297 A291094 A291965

Adjacent sequences: A248767 A248768 A248769 * A248771 A248772 A248773

Keyword

nonn,easy

Author

Clark Kimberling, Oct 14 2014

Status

approved