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A248773 Greatest 7th power integer that divides n!.

%I A248773 #6 Mar 12 2015 22:34:27
%S A248773 1,1,1,1,1,1,1,128,128,128,128,128,128,128,128,16384,16384,35831808,
%T A248773 35831808,35831808,35831808,35831808,35831808,4586471424,4586471424,
%U A248773 4586471424,4586471424,4586471424,4586471424,783641640960000000,783641640960000000
%N A248773 Greatest 7th power integer that divides n!.
%C A248773 Every term divides all its successors.
%H A248773 Clark Kimberling, <a href="/A248773/b248773.txt">Table of n, a(n) for n = 1..1000</a>
%F A248773 a(n) = n!/A248775(n).
%e A248773 a(8) = 128 because 128 divides 8! and if k > 2 then k^7 does not divide 8!.
%t A248773 z = 50; f[n_] := f[n] = FactorInteger[n!]; r[m_, x_] := r[m, x] = m*Floor[x/m];
%t A248773 u[n_] := Table[f[n][[i, 1]], {i, 1, Length[f[n]]}];
%t A248773 v[n_] := Table[f[n][[i, 2]], {i, 1, Length[f[n]]}];
%t A248773 p[m_, n_] := p[m, n] = Product[u[n][[i]]^r[m, v[n]][[i]], {i, 1, Length[f[n]]}];
%t A248773 m = 7; Table[p[m, n], {n, 1, z}]  (* A248773 *)
%t A248773 Table[p[m, n]^(1/m), {n, 1, z}]   (* A248774 *)
%t A248773 Table[n!/p[m, n], {n, 1, z}]      (* A248775 *)
%Y A248773 Cf. A248774, A248775, A000142.
%K A248773 nonn,easy
%O A248773 1,8
%A A248773 _Clark Kimberling_, Oct 14 2014