A023514 a(n) = sum of exponents in prime-power factorization of prime(n) + 1.

1, 2, 2, 3, 3, 2, 3, 3, 4, 3, 5, 2, 3, 3, 5, 4, 4, 2, 3, 5, 2, 5, 4, 4, 3, 3, 4, 5, 3, 3, 7, 4, 3, 4, 4, 4, 2, 3, 5, 3, 5, 3, 7, 2, 4, 5, 3, 6, 4, 3, 4, 6, 3, 5, 3, 5, 5, 5, 2, 3, 3, 4, 4, 5, 2, 3, 3, 3, 4, 4, 3, 6, 5, 3, 4, 8, 4, 2, 3, 3, 5, 2, 7, 3, 5, 4, 5, 2, 4, 5, 5, 7, 4, 4, 5, 6, 4, 4, 3

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A210934.

Cf. A000040, A001222.

Programs

Maple

with(numtheory):
a:= n-> add(i[2], i=ifactors(ithprime(n)+1)[2]):
seq(a(n), n=1..100);

Mathematica

Array[Plus@@Last/@FactorInteger[Prime[ # ]+1]&,6! ] (* Vladimir Joseph Stephan Orlovsky, Feb 28 2010 *)

PARI

a(n) = bigomega(prime(n)+1); \\ Michel Marcus, Jan 04 2016

Formula

a(n) = A001222(A000040(n)+1). - Zak Seidov, Jan 04 2016