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A248776 Greatest 8th power integer that divides n!

%I A248776 #8 Dec 23 2019 13:13:01
%S A248776 1,1,1,1,1,1,1,1,1,256,256,256,256,256,256,256,256,429981696,
%T A248776 429981696,429981696,429981696,429981696,429981696,429981696,
%U A248776 429981696,429981696,429981696,110075314176,110075314176,110075314176,110075314176,110075314176
%N A248776 Greatest 8th power integer that divides n!
%C A248776 Every term divides all its successors.
%H A248776 Clark Kimberling, <a href="/A248776/b248776.txt">Table of n, a(n) for n = 1..1000</a>
%F A248776 a(n) = n!/A248778(n).
%e A248776 a(8) = 128 because 128 divides 8! and if k > 2 then k^8 does not divide 8!.
%t A248776 z = 60; f[n_] := f[n] = FactorInteger[n!]; r[m_, x_] := r[m, x] = m*Floor[x/m];
%t A248776 u[n_] := Table[f[n][[i, 1]], {i, 1, Length[f[n]]}];
%t A248776 v[n_] := Table[f[n][[i, 2]], {i, 1, Length[f[n]]}];
%t A248776 p[m_, n_] := p[m, n] = Product[u[n][[i]]^r[m, v[n]][[i]], {i, 1, Length[f[n]]}];
%t A248776 m = 8; Table[p[m, n], {n, 1, z}]  (* A248776 *)
%t A248776 Table[p[m, n]^(1/m), {n, 1, z}]   (* A248777 *)
%t A248776 Table[n!/p[m, n], {n, 1, z}]      (* A248778 *)
%t A248776 Module[{e=Range[30]^8},Table[Max[Select[e,Divisible[n!,#]&]],{n,40}]] (* _Harvey P. Dale_, Dec 23 2019 *)
%Y A248776 Cf. A248777, A248778, A000142.
%K A248776 nonn,easy
%O A248776 1,10
%A A248776 _Clark Kimberling_, Oct 14 2014