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A248772 Greatest 6th-power-free divisor of n!.

%I A248772 #6 Mar 12 2015 23:27:55
%S A248772 1,2,6,24,120,720,5040,630,5670,56700,623700,7484400,97297200,
%T A248772 1362160800,28028000,7007000,119119000,2144142000,40738698000,
%U A248772 12730843125,267347705625,5881649523750,135277939046250,3246670537110000,5194672859376,135061494343776
%N A248772 Greatest 6th-power-free divisor of n!.
%H A248772 Clark Kimberling, <a href="/A248772/b248772.txt">Table of n, a(n) for n = 1..1000</a>
%F A248772 a(n) = n!/A248770(n).
%e A248772 a(8) = 630 because 630 divides 8! and if k > 630 divides 8!, then h^6 divides 8!/k for some h > 1.
%t A248772 z = 50; f[n_] := f[n] = FactorInteger[n!]; r[m_, x_] := r[m, x] = m*Floor[x/m];
%t A248772 u[n_] := Table[f[n][[i, 1]], {i, 1, Length[f[n]]}];
%t A248772 v[n_] := Table[f[n][[i, 2]], {i, 1, Length[f[n]]}];
%t A248772 p[m_, n_] := p[m, n] = Product[u[n][[i]]^r[m, v[n]][[i]], {i, 1, Length[f[n]]}];
%t A248772 m = 6; Table[p[m, n], {n, 1, z}]  (* A248770 *)
%t A248772 Table[p[m, n]^(1/m), {n, 1, z}]   (* A248771 *)
%t A248772 Table[n!/p[m, n], {n, 1, z}]      (* A248772 *)
%Y A248772 Cf. A248770, A248771, A000142.
%K A248772 nonn,easy
%O A248772 1,2
%A A248772 _Clark Kimberling_, Oct 14 2014