%I #4 Oct 19 2014 16:24:43
%S 1,1,1,1,1,2,2,2,6,12,12,12,12,12,12,24,24,144,144,720,720,720,720,
%T 1440,1440,1440,4320,60480,60480,60480,60480,120960,120960,241920,
%U 1209600,3628800,3628800,3628800,3628800,7257600
%N Greatest k such that k^4 divides n!
%C Every term divides all its successors.
%H Clark Kimberling, <a href="/A248765/b248765.txt">Table of n, a(n) for n = 1..1000</a>
%e a(6) = 2 because 2^4 divides 6! and if k > 2 then k^4 does not divide 6!.
%t z = 40; 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 = 4; Table[p[m, n], {n, 1, z}] (* A248764 *)
%t Table[p[m, n]^(1/m), {n, 1, z}] (* A248765 *)
%t Table[n!/p[m, n], {n, 1, z}] (* A248766 *)
%Y Cf. A248765, A248766, A248762, A000142.
%K nonn,easy
%O 1,6
%A _Clark Kimberling_, Oct 14 2014
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