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

1,4

Links

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A000142.

Sequence in context: A204992 A186726 A205405 * A130675 A319118 A163820

Adjacent sequences: A112620 A112621 A112622 * A112624 A112625 A112626

Keyword

nonn

Author

Leroy Quet, Dec 25 2005

Extensions

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

Status

approved