A057951 Number of prime factors of 10^n - 1 (counted with multiplicity).

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

Offset: 1

Author

Patrick De Geest, Nov 15 2000

Keywords

• nonn

Links

• Max Alekseyev, Table of n, a(n) for n = 1..352 (first 322 terms from Ray Chandler)
• Makoto Kamada, Factorizations of 11...11 (Repunit).
• S. S. Wagstaff, Jr., Main Tables from the Cunningham Project.
• S. S. Wagstaff, Jr., The Cunningham Project

Crossrefs

bigomega(b^n-1): this sequence (b=10), A057952 (b=9), A057953 (b=8), A057954 (b=7), A057955 (b=6), A057956 (b=5), A057957 (b=4), A057958 (b=3), A046051 (b=2).

Cf. A001222, A002283, A046053, A085035, A003020, A046107, A005422, A061075, A102380, A095370, A147556, A081317, A081318, A102347, A112505.

Programs

Mathematica

PrimeOmega[10^Range[70]-1] (* Jayanta Basu, May 29 2013 *)

PARI

a(n)=bigomega(10^n-1) \\ Charles R Greathouse IV, Sep 14 2015

Formula

Mobius transform of A085035 - T. D. Noe, Jun 19 2003

a(n) = Omega(10^n -1) = Omega(R_n) + 2 = A046053(n) + 2 {where Omega(n) = A001222(n) and R_n = (10^n - 1)/9 = A002275(n)}. - Lekraj Beedassy, Jun 09 2006

a(n) = A001222(A002283(n)). - Ray Chandler, Apr 22 2017

Extensions

Erroneous b-file replaced by Ray Chandler, Apr 26 2017