A248771 Greatest k such that k^6 divides n!

1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 6, 12, 12, 12, 12, 24, 24, 24, 24, 24, 120, 120, 360, 720, 720, 720, 720, 1440, 1440, 1440, 1440, 1440, 1440, 1440, 4320, 8640, 8640, 60480, 60480, 60480, 60480, 120960, 120960, 120960, 120960, 604800

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 2^6 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. A248770, A248772, A000142.

Sequence in context: A211455 A214079 A202742 * A339446 A339166 A359093

Adjacent sequences: A248768 A248769 A248770 * A248772 A248773 A248774

Keyword

nonn,easy

Author

Clark Kimberling, Oct 14 2014

Status

approved