cp's OEIS Frontend

A248778 Greatest 8th-power-free divisor of n!.

%I A248778 #6 Mar 12 2015 20:33:04
%S A248778 1,2,6,24,120,720,5040,40320,362880,14175,155925,1871100,24324300,
%T A248778 340540200,5108103000,81729648000,1389404016000,14889875,282907625,
%U A248778 5658152500,118821202500,2614066455000,60123528465000,1442964683160000,36074117079000000
%N A248778 Greatest 8th-power-free divisor of n!.
%H A248778 Clark Kimberling, <a href="/A248778/b248778.txt">Table of n, a(n) for n = 1..1000</a>
%F A248778 a(n) = n!/A248773(n).
%e A248778 a(8) = 315 because 315 divides 8! and if k > 315 divides 8!, then h^7 divides 8!/k for some h > 1.
%t A248778 z = 60; f[n_] := f[n] = FactorInteger[n!]; r[m_, x_] := r[m, x] = m*Floor[x/m];
%t A248778 u[n_] := Table[f[n][[i, 1]], {i, 1, Length[f[n]]}];
%t A248778 v[n_] := Table[f[n][[i, 2]], {i, 1, Length[f[n]]}];
%t A248778 p[m_, n_] := p[m, n] = Product[u[n][[i]]^r[m, v[n]][[i]], {i, 1, Length[f[n]]}];
%t A248778 m = 8; Table[p[m, n], {n, 1, z}]  (* A248776 *)
%t A248778 Table[p[m, n]^(1/m), {n, 1, z}]   (* A248777 *)
%t A248778 Table[n!/p[m, n], {n, 1, z}]      (* A248778 *)
%Y A248778 Cf. A248776, A248777, A000142.
%K A248778 nonn,easy
%O A248778 1,2
%A A248778 _Clark Kimberling_, Oct 14 2014