A248770 - OEIS

%I #6 Mar 12 2015 23:27:39

%S 1,1,1,1,1,1,1,64,64,64,64,64,64,64,46656,2985984,2985984,2985984,

%T 2985984,191102976,191102976,191102976,191102976,191102976,

%U 2985984000000,2985984000000,2176782336000000,139314069504000000,139314069504000000,139314069504000000

%N Greatest 6th power integer that divides n!.

%C Every term divides all its successors.

%H Clark Kimberling, <a href="/A248770/b248770.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = n!/A248772(n).

%e a(8) = 64 because 64 divides 8! and if k > 2 then k^6 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 = 6; Table[p[m, n], {n, 1, z}]  (* A248770 *)

%t Table[p[m, n]^(1/m), {n, 1, z}]   (* A248771 *)

%t Table[n!/p[m, n], {n, 1, z}]      (* A248772 *)

%Y Cf. A248771, A248772, A000142.

%K nonn,easy

%O 1,8

%A _Clark Kimberling_, Oct 14 2014