A057955 Number of prime factors of 6^n - 1 (counted with multiplicity).

1, 2, 2, 3, 3, 4, 2, 4, 4, 6, 3, 7, 3, 6, 6, 6, 5, 7, 3, 9, 4, 5, 5, 9, 6, 7, 6, 9, 2, 11, 3, 9, 6, 8, 7, 13, 6, 6, 6, 12, 3, 10, 5, 9, 11, 8, 4, 13, 5, 10, 9, 11, 4, 11, 7, 14, 7, 6, 4, 20, 4, 5, 10, 12, 9, 12, 3, 11, 8, 18, 2, 18, 5, 10, 12, 9, 6, 15, 4, 17, 8, 7, 8, 17, 10, 7, 7, 12, 4, 18, 6

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..420

S. S. Wagstaff, Jr., The Cunningham Project

Formula

Möbius transform of A085031. - T. D. Noe, Jun 19 2003

a(n) = A001222(A024062(n)). - Amiram Eldar, Feb 02 2020

Example

6^10 - 1 = 60466175 = 5^2 * 7 * 11 * 101 * 311 and a(10) = bigomega(60466175) = 2+1+1+1+1 = 6. - Bernard Schott, Feb 02 2020

Mathematica

PrimeOmega[6^Range[100]-1] (* Harvey P. Dale, Dec 14 2015 *)

Prog

(Magma) f:=func<n|&+[p[2]: p in Factorization(n)]>; [f(6^n - 1):n in [1..90]]; // Marius A. Burtea, Feb 02 2020

Crossrefs

bigomega(b^n-1): A057951 (b=10), A057952 (b=9), A057953 (b=8), A057954 (b=7), this sequence (b=6), A057956 (b=5), A057957 (b=4), A057958 (b=3), A046051 (b=2).

Cf. A001222, A024062, A085031, A274907.

Sequence in context: A337776 A366611 A091220 * A305788 A116473 A341151

Adjacent sequences: A057952 A057953 A057954 * A057956 A057957 A057958

Keyword

nonn

Author

Patrick De Geest, Nov 15 2000

Status

approved