A023508 Sum of exponents in prime-power factorization of n-th prime - 1.

0, 1, 2, 2, 2, 3, 4, 3, 2, 3, 3, 4, 4, 3, 2, 3, 2, 4, 3, 3, 5, 3, 2, 4, 6, 4, 3, 2, 5, 5, 4, 3, 4, 3, 3, 4, 4, 5, 2, 3, 2, 5, 3, 7, 4, 4, 4, 3, 2, 4, 4, 3, 6, 4, 8, 2, 3, 5, 4, 5, 3, 3, 4, 3, 5, 3, 4, 6, 2, 4, 6, 2, 3, 4, 5, 2, 3, 5, 6, 5, 3, 5, 3, 7, 3, 3, 7, 5, 4, 4, 2, 2, 6, 4, 3, 2, 3, 5, 4

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• easy

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001222, A008334, A006093, A210936.

Programs

Mathematica

Array[Plus@@Last/@FactorInteger[Prime[ # ]-1]&,6! ] (* Vladimir Joseph Stephan Orlovsky, Feb 28 2010 *)
PrimeOmega[Prime[Range[100]] - 1] (* Amiram Eldar, Apr 16 2024 *)

PARI

a(n) = bigomega(prime(n)-1); \\ Amiram Eldar, Apr 16 2024

Formula

a(n) = A001222(A006093(n)). - R. J. Mathar, Feb 06 2019