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%I #4 Oct 19 2014 16:24:14
%S 1,1,1,1,1,1,1,2,2,2,2,12,12,12,12,24,24,24,24,24,24,24,24,144,720,
%T 720,720,1440,1440,1440,1440,2880,8640,8640,60480,60480,60480,120960,
%U 120960,120960,120960,120960,120960,241920,3628800,3628800,3628800,7257600
%N Greatest k such that k^5 divides n!
%C Every term divides all its successors.
%H Clark Kimberling, <a href="/A248768/b248768.txt">Table of n, a(n) for n = 1..1000</a>
%e a(8) = 2 because 2^5 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. A248767, A248769, A000142.
%K nonn,easy
%O 1,8
%A _Clark Kimberling_, Oct 14 2014
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