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

1,2

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

Formula

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

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

Mathematica

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

Prog

(Magma) f:=func<n|&+[p[2]: p in Factorization(n)]>; [f(8^n - 1):n in [1..90]]; // Marius A. Burtea, Feb 02 2020

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.

Sequence in context: A057958 A225411 A247815 * A372679 A129231 A166477

Adjacent sequences: A057950 A057951 A057952 * A057954 A057955 A057956

Keyword

nonn

Author

Patrick De Geest, Nov 15 2000

Status

approved