A057957 Number of prime factors of 4^n - 1 (counted with multiplicity).

1, 2, 3, 3, 3, 5, 3, 4, 6, 6, 4, 7, 3, 6, 7, 5, 3, 10, 3, 8, 8, 7, 4, 10, 7, 7, 9, 8, 6, 13, 3, 7, 9, 7, 9, 14, 5, 7, 8, 10, 5, 14, 5, 10, 13, 9, 6, 13, 5, 14, 11, 10, 6, 15, 12, 11, 9, 9, 6, 17, 3, 8, 14, 9, 9, 15, 5, 11, 9, 16, 6, 19, 6, 10, 14, 11, 10, 18, 5, 13, 16, 10, 8, 19, 7, 10, 11

Offset: 1

Author

Patrick De Geest, Nov 15 2000

Keywords

• nonn

Links

• Max Alekseyev, Table of n, a(n) for n = 1..1128 (first 603 terms from Amiram Eldar)
• S. S. Wagstaff, Jr., The Cunningham Project

Crossrefs

bigomega(b^n-1): A057951 (b=10), A057952 (b=9), A057953 (b=8), A057954 (b=7), A057955 (b=6), A057956 (b=5), this sequence (b=4), A057958 (b=3), A046051 (b=2).

Cf. A001222, A024036, A054992, A085029, A274906.

Programs

Mathematica

PrimeOmega/@(4^Range[90]-1) (* Harvey P. Dale, Dec 31 2018 *)

Formula

Mobius transform of A085029. - T. D. Noe, Jun 19 2003

a(n) = A001222(A024036(n)) = A046051(2*n). - Amiram Eldar, Feb 01 2020