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

Author

Patrick De Geest, Nov 15 2000

Keywords

• nonn

Examples

			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
		

Links

• Max Alekseyev, Table of n, a(n) for n = 1..430 (terms 1..420 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), this sequence (b=6), A057956 (b=5), A057957 (b=4), A057958 (b=3), A046051 (b=2).

Cf. A001222, A024062, A085031, A274907.

Programs

Magma

f:=func; [f(6^n - 1):n in [1..90]]; // Marius A. Burtea, Feb 02 2020

Mathematica

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

Formula

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

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