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%I #6 Mar 14 2015 10:09:44
%S 1,2,6,24,120,45,315,2520,280,175,1925,23100,300300,4204200,63063000,
%T 63063000,1072071000,14889875,282907625,9053044,190113924,4182506328,
%U 96197645544,144296468316,3607411707900,93792704405400,31264234801800,22787343150,660832951350
%N Greatest 4th-power-free divisor of n!
%H Clark Kimberling, <a href="/A248766/b248766.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = n!/A248764(n).
%e a(6) = 45 because 45 divides 6! and if k > 45 divides 6!, then h^4 divides 6!/k for some h > 1.
%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. A248764, A248765, A000142.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Oct 14 2014
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