A248769 Greatest 5th-power-free divisor of n!.

1, 2, 6, 24, 120, 720, 5040, 1260, 11340, 113400, 1247400, 1925, 25025, 350350, 5255250, 2627625, 44669625, 804053250, 15277011750, 305540235000, 6416344935000, 141159588570000, 3246670537110000, 10020588077500, 80164704620, 2084282320120, 56275622643240

Offset

1,2

Links

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

Formula

a(n) = n!/A248767(n).

Example

a(8) = 1260 because 1260 divides 8! and if k > 1260 divides 8!, then h^5 divides 8!/k for some h > 1.

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 = 5; Table[p[m, n], {n, 1, z}]  (* A248767 *)
Table[p[m, n]^(1/m), {n, 1, z}]   (* A248768 *)
Table[n!/p[m, n], {n, 1, z}]      (* A248769 *)

Crossrefs

Cf. A248767, A248768, A000142.

Sequence in context: A108889 A248772 A033645 * A319547 A319208 A276841

Adjacent sequences: A248766 A248767 A248768 * A248770 A248771 A248772

Keyword

nonn,easy

Author

Clark Kimberling, Oct 14 2014

Status

approved