A112623 If p^b(p,n) is the highest power of the prime p dividing n, then a(n) = sum_{p|n} b(p,n)!.

0, 1, 1, 2, 1, 2, 1, 6, 2, 2, 1, 3, 1, 2, 2, 24, 1, 3, 1, 3, 2, 2, 1, 7, 2, 2, 6, 3, 1, 3, 1, 120, 2, 2, 2, 4, 1, 2, 2, 7, 1, 3, 1, 3, 3, 2, 1, 25, 2, 3, 2, 3, 1, 7, 2, 7, 2, 2, 1, 4, 1, 2, 3, 720, 2, 3, 1, 3, 2, 3, 1, 8, 1, 2, 3, 3, 2, 3, 1, 25, 24, 2, 1, 4, 2, 2, 2, 7, 1, 4, 2, 3, 2, 2, 2, 121, 1, 3, 3, 4, 1

Offset: 1

Author

Leroy Quet, Dec 25 2005

Keywords

• nonn

Examples

			45 = 3^2 * 5^1. So a(45) = 2! + 1! = 3.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000142.

Programs

Mathematica

f[n_] := Block[{fi = Last@Transpose@FactorInteger@n}, Plus @@ (fi!)]; Array[f, 101] (* Robert G. Wilson v, Dec 27 2005 *)

PARI

A112623(n) = { my(f = factor(n)); my(s = 0); for (k=1, #f~, s = s + f[k, 2]!; ); s; } \\ Antti Karttunen, May 25 2017

Extensions

More terms from Robert G. Wilson v, Dec 27 2005