A248767 - OEIS

%I #6 Mar 13 2015 18:49:10

%S 1,1,1,1,1,1,1,32,32,32,32,248832,248832,248832,248832,7962624,

%T 7962624,7962624,7962624,7962624,7962624,7962624,7962624,61917364224,

%U 193491763200000,193491763200000,193491763200000,6191736422400000,6191736422400000,6191736422400000

%N Greatest 5th power integer that divides n!.

%C Every term divides all its successors.

%H Clark Kimberling, <a href="/A248767/b248767.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = n!/A248769(n).

%e a(8) = 32 because 32 divides 8! and if k > 2 then k^5 does not divide 8!.

%t z = 50; 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 = 5; Table[p[m, n], {n, 1, z}]  (* A248767 *)

%t Table[p[m, n]^(1/m), {n, 1, z}]   (* A248768 *)

%t Table[n!/p[m, n], {n, 1, z}]      (* A248769 *)

%Y Cf. A248768, A248769, A000142.

%K nonn,easy

%O 1,8

%A _Clark Kimberling_, Oct 14 2014