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

1,1

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

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

Mathematica

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

Prog

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

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.

Sequence in context: A344351 A108355 A346049 * A076410 A361164 A309941

Adjacent sequences: A057948 A057949 A057950 * A057952 A057953 A057954

Keyword

nonn

Author

Patrick De Geest, Nov 15 2000

Extensions

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

Status

approved