A057952 Number of prime factors of 9^n - 1 (counted with multiplicity).

3, 5, 5, 7, 6, 8, 5, 10, 8, 10, 7, 11, 5, 9, 11, 12, 8, 12, 7, 13, 11, 11, 6, 17, 10, 9, 13, 13, 9, 17, 8, 14, 12, 12, 11, 16, 8, 11, 15, 18, 8, 18, 6, 16, 19, 10, 10, 21, 12, 18, 15, 13, 8, 18, 15, 19, 15, 13, 7, 24, 7, 13, 19, 16, 12, 18, 8, 17, 15, 20, 9, 24, 9, 13, 22, 17, 13, 22

Offset: 1

Author

Patrick De Geest, Nov 15 2000

Keywords

• nonn

Links

• Max Alekseyev, Table of n, a(n) for n = 1..690 (first 330 terms from Amiram Eldar)
• S. S. Wagstaff, Jr., The Cunningham Project

Crossrefs

bigomega(b^n-1): A046051 (b=2), A057958 (b=3), A057957 (b=4), A057956 (b=5), A057955 (b=6), A057954 (b=7), A057953 (b=8), this sequence (b=9), A057951 (b=10), A366682 (b=11), A366708 (b=12).

Cf. A001222, A002591, A024101, A074477, A085034, A133801, A274909, A366660, A366661, A366662.

Programs

Mathematica

PrimeOmega[Table[9^n - 1, {n, 1, 30}]] (* Amiram Eldar, Feb 02 2020 *)

Formula

Mobius transform of A085034. - T. D. Noe, Jun 19 2003

a(n) = A001222(A024101(n)) = A057958(2*n). - Amiram Eldar, Feb 02 2020

a(n) = A057941(n) + A057958(n). - Max Alekseyev, Jan 07 2024