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A248771 Greatest k such that k^6 divides n!

%I A248771 #4 Oct 19 2014 16:23:48
%S A248771 1,1,1,1,1,1,1,2,2,2,2,2,2,2,6,12,12,12,12,24,24,24,24,24,120,120,360,
%T A248771 720,720,720,720,1440,1440,1440,1440,1440,1440,1440,4320,8640,8640,
%U A248771 60480,60480,60480,60480,120960,120960,120960,120960,604800
%N A248771 Greatest k such that k^6 divides n!
%C A248771 Every term divides all its successors.
%H A248771 Clark Kimberling, <a href="/A248771/b248771.txt">Table of n, a(n) for n = 1..1000</a>
%e A248771 a(8) = 2 because 2^6 divides 8! and if k > 2 then k^6 does not divide 8!.
%t A248771 z = 50; f[n_] := f[n] = FactorInteger[n!]; r[m_, x_] := r[m, x] = m*Floor[x/m];
%t A248771 u[n_] := Table[f[n][[i, 1]], {i, 1, Length[f[n]]}];
%t A248771 v[n_] := Table[f[n][[i, 2]], {i, 1, Length[f[n]]}];
%t A248771 p[m_, n_] := p[m, n] = Product[u[n][[i]]^r[m, v[n]][[i]], {i, 1, Length[f[n]]}];
%t A248771 m = 6; Table[p[m, n], {n, 1, z}]  (* A248770 *)
%t A248771 Table[p[m, n]^(1/m), {n, 1, z}]   (* A248771 *)
%t A248771 Table[n!/p[m, n], {n, 1, z}]      (* A248772 *)
%Y A248771 Cf. A248770, A248772, A000142.
%K A248771 nonn,easy
%O A248771 1,8
%A A248771 _Clark Kimberling_, Oct 14 2014