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A248762 Greatest cube that divides n!. 5
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 (list; graph; refs; listen; history; text; internal format)
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 *)

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

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Last modified June 28 03:21 EDT 2017. Contains 288813 sequences.