A057936 Number of prime factors of 8^n + 1 (counted with multiplicity).

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

Offset: 1

Author

Patrick De Geest, Oct 15 2000

Keywords

• nonn

Links

• Max Alekseyev, Table of n, a(n) for n = 1..502 (first 354 terms from Amiram Eldar)
• S. S. Wagstaff, Jr., The Cunningham Project

Crossrefs

bigomega(b^n+1): A057934 (b=10), A057935 (b=9), this sequence (b=8), A057937 (b=7), A057938 (b=6), A057939 (b=5), A057940 (b=4), A057941 (b=3), A054992 (b=2).

Cf. A001222, A057953, A062395, A274905.

Programs

Magma

f:=func; [f(8^n + 1):n in [1..110]]; // Marius A. Burtea, Feb 02 2020

Mathematica

PrimeOmega[8^Range[100]+1] (* Harvey P. Dale, Dec 16 2014 *)

Formula

a(n) = A057953(2n) - A057953(n). - T. D. Noe, Jun 19 2003

a(n) = A001222(A062395(n)) = A054992(3*n). - Amiram Eldar, Feb 02 2020