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