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