A248763 Greatest k such that k^3 divides n!

1, 1, 1, 2, 2, 2, 2, 4, 12, 12, 12, 24, 24, 24, 360, 1440, 1440, 1440, 1440, 2880, 60480, 60480, 60480, 120960, 604800, 604800, 1814400, 3628800, 3628800, 3628800, 3628800, 14515200, 479001600, 479001600, 479001600, 958003200, 958003200, 958003200

Offset

1,4

Comments

Every term divides all its successors.

Links

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

Example

a(4) = 2 because 2^3 divides 24 and if k > 2, then k^3 > 8 does not divide 24.

Mathematica

z = 40; 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 = 3; Table[p[m, n], {n, 1, z}]  (* A248762 *)
Table[p[m, n]^(1/m), {n, 1, z}]   (* A248763 *)
Table[n!/p[m, n], {n, 1, z}]      (* A145642 *)

Crossrefs

Cf. A248762, A145642, A000142.

Sequence in context: A360315 A045948 A278110 * A233585 A103512 A130086

Adjacent sequences: A248760 A248761 A248762 * A248764 A248765 A248766

Keyword

nonn,easy

Author

Clark Kimberling, Oct 14 2014

Status

approved