A248766 Greatest 4th-power-free divisor of n!

1, 2, 6, 24, 120, 45, 315, 2520, 280, 175, 1925, 23100, 300300, 4204200, 63063000, 63063000, 1072071000, 14889875, 282907625, 9053044, 190113924, 4182506328, 96197645544, 144296468316, 3607411707900, 93792704405400, 31264234801800, 22787343150, 660832951350

Offset

1,2

Links

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

Formula

a(n) = n!/A248764(n).

Example

a(6) = 45 because 45 divides 6! and if k > 45 divides 6!, then h^4 divides 6!/k for some h > 1.

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 = 4; Table[p[m, n], {n, 1, z}]  (* A248764 *)
Table[p[m, n]^(1/m), {n, 1, z}]   (* A248765 *)
Table[n!/p[m, n], {n, 1, z}]      (* A248766 *)

Crossrefs

Cf. A248764, A248765, A000142.

Sequence in context: A360298 A033643 A050211 * A263713 A242427 A319545

Adjacent sequences: A248763 A248764 A248765 * A248767 A248768 A248769

Keyword

nonn,easy

Author

Clark Kimberling, Oct 14 2014

Status

approved