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A248775 Greatest 7th-power-free divisor of n!.

%I A248775 #6 Mar 12 2015 22:34:06
%S A248775 1,2,6,24,120,720,5040,315,2835,28350,311850,3742200,48648600,
%T A248775 681080400,10216206000,1277025750,21709437750,178678500,3394891500,
%U A248775 67897830000,1425854430000,31368797460000,721482341580000,135277939046250,3381948476156250
%N A248775 Greatest 7th-power-free divisor of n!.
%H A248775 Clark Kimberling, <a href="/A248775/b248775.txt">Table of n, a(n) for n = 1..1000</a>
%F A248775 a(n) = n!/A248773(n).
%e A248775 a(8) = 315 because 315 divides 8! and if k > 315 divides 8!, then h^7 divides 8!/k for some h > 1.
%t A248775 z = 50; f[n_] := f[n] = FactorInteger[n!]; r[m_, x_] := r[m, x] = m*Floor[x/m];
%t A248775 u[n_] := Table[f[n][[i, 1]], {i, 1, Length[f[n]]}];
%t A248775 v[n_] := Table[f[n][[i, 2]], {i, 1, Length[f[n]]}];
%t A248775 p[m_, n_] := p[m, n] = Product[u[n][[i]]^r[m, v[n]][[i]], {i, 1, Length[f[n]]}];
%t A248775 m = 7; Table[p[m, n], {n, 1, z}]  (* A248773 *)
%t A248775 Table[p[m, n]^(1/m), {n, 1, z}]   (* A248774 *)
%t A248775 Table[n!/p[m, n], {n, 1, z}]      (* A248775 *)
%Y A248775 Cf. A248773, A248774, A000142.
%K A248775 nonn,easy
%O A248775 1,2
%A A248775 _Clark Kimberling_, Oct 14 2014