A057938 Number of prime factors of 6^n + 1 (counted with multiplicity).

1, 1, 2, 1, 3, 3, 4, 2, 3, 3, 2, 2, 4, 3, 5, 3, 3, 6, 3, 3, 6, 4, 3, 4, 4, 4, 5, 5, 4, 9, 2, 3, 6, 3, 11, 5, 4, 3, 9, 5, 4, 7, 2, 3, 7, 5, 2, 7, 7, 6, 8, 4, 5, 10, 8, 6, 7, 3, 2, 6, 3, 2, 10, 3, 8, 11, 5, 5, 6, 7, 4, 5, 6, 5, 10, 5, 6, 11, 6, 6, 8, 4, 5, 8, 8, 5, 11, 4, 3, 16, 12, 4, 5, 5, 10, 4, 4, 5

Offset

1,3

Links

Max Alekseyev, Table of n, a(n) for n = 1..420 (first 408 terms from Amiram Eldar)

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

Formula

a(n) = A057955(2n) - A057955(n). - T. D. Noe, Jun 19 2003

a(n) = A001222(A062394(n)). - Amiram Eldar, Feb 02 2020

Mathematica

PrimeOmega[6^Range[100]+1] (* Harvey P. Dale, Mar 10 2013 *)

Prog

(Magma) f:=func<n|&+[p[2]: p in Factorization(n)]>; [f(6^n + 1):n in [1..100]]; // Marius A. Burtea, Feb 02 2020

Crossrefs

bigomega(b^n+1): A057934 (b=10), A057935 (b=9), A057936 (b=8), A057937 (b=7), this sequence (b=6), A057939 (b=5), A057940 (b=4), A057941 (b=3), A054992 (b=2).

Cf. A001222, A057955, A062394, A274904.

Sequence in context: A082666 A363619 A363625 * A375729 A144623 A340284

Adjacent sequences: A057935 A057936 A057937 * A057939 A057940 A057941

Keyword

nonn

Author

Patrick De Geest, Oct 15 2000

Status

approved