A248777 Greatest k such that k^8 divides n!

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 24, 24, 24, 24, 24, 24, 48, 240, 720, 720, 720, 720, 720, 720, 720, 720, 1440, 1440, 1440, 1440, 1440, 10080, 10080, 10080, 20160, 20160, 60480, 60480, 60480, 60480

Offset: 1

Author

Clark Kimberling, Oct 14 2014

Keywords

• nonn
• easy

Comments

Every term divides all its successors.

Examples

			a(10) = 2 because 2^10 divides 8! and if k > 2 then k^8 does not divide 8!.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A248776, A248778, A000142.

Programs

Mathematica

z = 60; f[n_] := f[n] = FactorInteger[n!]; r[m_, x_] := r[m, x] = m*Floor[x/m];
u[n_] := Table[f[n][[i, 1]], {i, 1, Length[f[n]]}];
v[n_] := Table[f[n][[i, 2]], {i, 1, Length[f[n]]}];
p[m_, n_] := p[m, n] = Product[u[n][[i]]^r[m, v[n]][[i]], {i, 1, Length[f[n]]}];
m = 8; Table[p[m, n], {n, 1, z}]  (* A248776 *)
Table[p[m, n]^(1/m), {n, 1, z}]   (* A248777 *)
Table[n!/p[m, n], {n, 1, z}]      (* A248778 *)