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A248777 Greatest k such that k^8 divides n!

%I A248777 #5 Oct 19 2014 16:22:46
%S A248777 1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,12,12,12,12,12,12,12,12,12,12,24,
%T A248777 24,24,24,24,24,48,240,720,720,720,720,720,720,720,720,1440,1440,1440,
%U A248777 1440,1440,10080,10080,10080,20160,20160,60480,60480,60480,60480
%N A248777 Greatest k such that k^8 divides n!
%C A248777 Every term divides all its successors.
%H A248777 Clark Kimberling, <a href="/A248777/b248777.txt">Table of n, a(n) for n = 1..1000</a>
%e A248777 a(10) = 2 because 2^10 divides 8! and if k > 2 then k^8 does not divide 8!.
%t A248777 z = 60; f[n_] := f[n] = FactorInteger[n!]; r[m_, x_] := r[m, x] = m*Floor[x/m];
%t A248777 u[n_] := Table[f[n][[i, 1]], {i, 1, Length[f[n]]}];
%t A248777 v[n_] := Table[f[n][[i, 2]], {i, 1, Length[f[n]]}];
%t A248777 p[m_, n_] := p[m, n] = Product[u[n][[i]]^r[m, v[n]][[i]], {i, 1, Length[f[n]]}];
%t A248777 m = 8; Table[p[m, n], {n, 1, z}]  (* A248776 *)
%t A248777 Table[p[m, n]^(1/m), {n, 1, z}]   (* A248777 *)
%t A248777 Table[n!/p[m, n], {n, 1, z}]      (* A248778 *)
%Y A248777 Cf. A248776, A248778, A000142.
%K A248777 nonn,easy
%O A248777 1,10
%A A248777 _Clark Kimberling_, Oct 14 2014