A057935 Number of prime factors of 9^n + 1 (counted with multiplicity).

2, 2, 3, 3, 4, 3, 4, 2, 4, 3, 4, 6, 4, 4, 6, 2, 4, 4, 4, 5, 7, 5, 4, 4, 8, 4, 5, 6, 4, 7, 5, 2, 6, 5, 9, 8, 5, 6, 7, 5, 5, 10, 7, 6, 9, 4, 4, 6, 9, 6, 8, 7, 6, 9, 8, 9, 9, 5, 3, 11, 6, 4, 11, 6, 8, 9, 9, 8, 6, 9, 5, 6, 6, 6, 13, 4, 8, 7, 5, 4, 7, 6, 5, 11, 8, 5, 8, 7, 4, 11, 7, 9, 9, 5, 9, 7, 5, 6, 10, 7, 6

Offset

1,1

Links

Max Alekseyev, Table of n, a(n) for n = 1..345 (first 329 terms from Amiram Eldar)

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

Formula

a(n) = A057952(2n) - A057952(n). - T. D. Noe, Jun 19 2003

a(n) = A001222(A062396(n)) = A057941(2*n). - Amiram Eldar, Feb 02 2020

Mathematica

PrimeOmega[Table[9^n + 1, {n, 1, 30}]] (* Amiram Eldar, Feb 02 2020 *)

Prog

(Magma) f:=func<n|&+[p[2]: p in Factorization(n)]>; [f(9^n + 1):n in [1..100]]; // Marius A. Burtea, Feb 02 2020

Crossrefs

bigomega(b^n+1): A057934 (b=10), this sequence (b=9), A057936 (b=8), A057937 (b=7), A057938 (b=6), A057939 (b=5), A057940 (b=4), A057941 (b=3), A054992 (b=2).

Cf. A002592, A046053, A001222, A057941, A057952, A062396.

Sequence in context: A324863 A332894 A269989 * A292042 A282715 A124831

Adjacent sequences: A057932 A057933 A057934 * A057936 A057937 A057938

Keyword

nonn

Author

Patrick De Geest, Oct 15 2000

Status

approved