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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)!.
3
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
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
KEYWORD
nonn
AUTHOR
Leroy Quet, Dec 25 2005
EXTENSIONS
More terms from Robert G. Wilson v, Dec 27 2005
STATUS
approved