A248775 Greatest 7th-power-free divisor of n!.

1, 2, 6, 24, 120, 720, 5040, 315, 2835, 28350, 311850, 3742200, 48648600, 681080400, 10216206000, 1277025750, 21709437750, 178678500, 3394891500, 67897830000, 1425854430000, 31368797460000, 721482341580000, 135277939046250, 3381948476156250

Offset

1,2

Links

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

Formula

a(n) = n!/A248773(n).

Example

a(8) = 315 because 315 divides 8! and if k > 315 divides 8!, then h^7 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 = 7; Table[p[m, n], {n, 1, z}]  (* A248773 *)
Table[p[m, n]^(1/m), {n, 1, z}]   (* A248774 *)
Table[n!/p[m, n], {n, 1, z}]      (* A248775 *)

Crossrefs

Cf. A248773, A248774, A000142.

Sequence in context: A052399 A177553 A090583 * A108889 A248772 A033645

Adjacent sequences: A248772 A248773 A248774 * A248776 A248777 A248778

Keyword

nonn,easy

Author

Clark Kimberling, Oct 14 2014

Status

approved