A248762 Greatest cube that divides n!.

1, 1, 1, 8, 8, 8, 8, 64, 1728, 1728, 1728, 13824, 13824, 13824, 46656000, 2985984000, 2985984000, 2985984000, 2985984000, 23887872000, 221225582592000, 221225582592000, 221225582592000, 1769804660736000, 221225582592000000, 221225582592000000

Offset

1,4

Comments

Every term divides all its successors.

Links

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

Formula

a(n) = n!/A145642(n).

Example

a(4) = 8 because 8 divides 24 and if k > 2 then k^3 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 *)
gk[n_]:=Select[Divisors[n!], IntegerQ[Surd[#, 3]]&]; Max[#]&/@Array[gk, 30] (* Harvey P. Dale, Sep 16 2021 *)

Prog

(PARI) a(n)=k=ceil((n!/2)^(1/3)); while(n!%k^3, k--); k^3
vector(20, n, a(n)) \\ Derek Orr, Oct 19 2014

Crossrefs

Cf. A248763, A145642, A000142.

Sequence in context: A216412 A166082 A145446 * A186985 A203127 A023415

Adjacent sequences: A248759 A248760 A248761 * A248763 A248764 A248765

Keyword

nonn,easy

Author

Clark Kimberling, Oct 14 2014

Status

approved