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%I #6 Mar 13 2015 18:48:15
%S 1,2,6,24,120,720,5040,1260,11340,113400,1247400,1925,25025,350350,
%T 5255250,2627625,44669625,804053250,15277011750,305540235000,
%U 6416344935000,141159588570000,3246670537110000,10020588077500,80164704620,2084282320120,56275622643240
%N Greatest 5th-power-free divisor of n!.
%H Clark Kimberling, <a href="/A248769/b248769.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = n!/A248767(n).
%e a(8) = 1260 because 1260 divides 8! and if k > 1260 divides 8!, then h^5 divides 8!/k for some h > 1.
%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, A248768, A000142.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Oct 14 2014
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