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

1,10

Comments

Every term divides all its successors.

Links

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

Example

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

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 *)

Crossrefs

Cf. A248776, A248778, A000142.

Sequence in context: A330487 A339169 A171818 * A175101 A001991 A305706

Adjacent sequences: A248774 A248775 A248776 * A248778 A248779 A248780

Keyword

nonn,easy

Author

Clark Kimberling, Oct 14 2014

Status

approved