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A248770 Greatest 6th power integer that divides n!.

%I A248770 #6 Mar 12 2015 23:27:39
%S A248770 1,1,1,1,1,1,1,64,64,64,64,64,64,64,46656,2985984,2985984,2985984,
%T A248770 2985984,191102976,191102976,191102976,191102976,191102976,
%U A248770 2985984000000,2985984000000,2176782336000000,139314069504000000,139314069504000000,139314069504000000
%N A248770 Greatest 6th power integer that divides n!.
%C A248770 Every term divides all its successors.
%H A248770 Clark Kimberling, <a href="/A248770/b248770.txt">Table of n, a(n) for n = 1..1000</a>
%F A248770 a(n) = n!/A248772(n).
%e A248770 a(8) = 64 because 64 divides 8! and if k > 2 then k^6 does not divide 8!.
%t A248770 z = 50; f[n_] := f[n] = FactorInteger[n!]; r[m_, x_] := r[m, x] = m*Floor[x/m];
%t A248770 u[n_] := Table[f[n][[i, 1]], {i, 1, Length[f[n]]}];
%t A248770 v[n_] := Table[f[n][[i, 2]], {i, 1, Length[f[n]]}];
%t A248770 p[m_, n_] := p[m, n] = Product[u[n][[i]]^r[m, v[n]][[i]], {i, 1, Length[f[n]]}];
%t A248770 m = 6; Table[p[m, n], {n, 1, z}]  (* A248770 *)
%t A248770 Table[p[m, n]^(1/m), {n, 1, z}]   (* A248771 *)
%t A248770 Table[n!/p[m, n], {n, 1, z}]      (* A248772 *)
%Y A248770 Cf. A248771, A248772, A000142.
%K A248770 nonn,easy
%O A248770 1,8
%A A248770 _Clark Kimberling_, Oct 14 2014