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A248767 Greatest 5th power integer that divides n!.

%I A248767 #6 Mar 13 2015 18:49:10
%S A248767 1,1,1,1,1,1,1,32,32,32,32,248832,248832,248832,248832,7962624,
%T A248767 7962624,7962624,7962624,7962624,7962624,7962624,7962624,61917364224,
%U A248767 193491763200000,193491763200000,193491763200000,6191736422400000,6191736422400000,6191736422400000
%N A248767 Greatest 5th power integer that divides n!.
%C A248767 Every term divides all its successors.
%H A248767 Clark Kimberling, <a href="/A248767/b248767.txt">Table of n, a(n) for n = 1..1000</a>
%F A248767 a(n) = n!/A248769(n).
%e A248767 a(8) = 32 because 32 divides 8! and if k > 2 then k^5 does not divide 8!.
%t A248767 z = 50; f[n_] := f[n] = FactorInteger[n!]; r[m_, x_] := r[m, x] = m*Floor[x/m];
%t A248767 u[n_] := Table[f[n][[i, 1]], {i, 1, Length[f[n]]}];
%t A248767 v[n_] := Table[f[n][[i, 2]], {i, 1, Length[f[n]]}];
%t A248767 p[m_, n_] := p[m, n] = Product[u[n][[i]]^r[m, v[n]][[i]], {i, 1, Length[f[n]]}];
%t A248767 m = 5; Table[p[m, n], {n, 1, z}]  (* A248767 *)
%t A248767 Table[p[m, n]^(1/m), {n, 1, z}]   (* A248768 *)
%t A248767 Table[n!/p[m, n], {n, 1, z}]      (* A248769 *)
%Y A248767 Cf. A248768, A248769, A000142.
%K A248767 nonn,easy
%O A248767 1,8
%A A248767 _Clark Kimberling_, Oct 14 2014