A057953 Number of prime factors of 8^n - 1 (counted with multiplicity).

1, 3, 2, 5, 3, 6, 4, 7, 3, 7, 4, 10, 4, 8, 6, 10, 5, 9, 4, 13, 7, 9, 4, 14, 7, 8, 6, 14, 6, 13, 3, 13, 8, 11, 11, 15, 6, 9, 9, 17, 5, 14, 5, 15, 10, 9, 6, 19, 7, 14, 8, 18, 8, 16, 10, 19, 7, 11, 6, 24, 5, 8, 10, 16, 8, 17, 6, 20, 9, 22, 7, 21, 7, 13, 14, 17, 10, 16, 8, 23, 10, 12, 5, 24

Offset: 1

Author

Patrick De Geest, Nov 15 2000

Keywords

• nonn

Links

• Max Alekseyev, Table of n, a(n) for n = 1..500 (first 402 terms from Amiram Eldar)
• S. S. Wagstaff, Jr., The Cunningham Project

Crossrefs

bigomega(b^n-1): A057951 (b=10), A057952 (b=9), this sequence (b=8), A057954 (b=7), A057955 (b=6), A057956 (b=5), A057957 (b=4), A057958 (b=3), A046051 (b=2).

Cf. A001222, A024088, A085033, A274908.

Programs

Magma

f:=func; [f(8^n - 1):n in [1..90]]; // Marius A. Burtea, Feb 02 2020

Mathematica

PrimeOmega/@(8^Range[90]-1) (* Harvey P. Dale, May 24 2018 *)

Formula

Mobius transform of A085033. - T. D. Noe, Jun 19 2003

a(n) = A001222(A024088(n)) = A046051(3*n). - Amiram Eldar, Feb 02 2020