A057940 Number of prime factors of 4^n + 1 (counted with multiplicity).

1, 1, 2, 1, 3, 2, 3, 1, 4, 2, 3, 3, 4, 2, 6, 2, 4, 4, 4, 2, 6, 3, 5, 3, 7, 3, 6, 3, 3, 4, 5, 2, 6, 4, 7, 5, 5, 4, 10, 3, 5, 5, 5, 4, 11, 2, 4, 3, 6, 6, 9, 2, 4, 6, 7, 5, 8, 3, 7, 6, 6, 4, 10, 2, 10, 7, 6, 4, 8, 4, 6, 7, 5, 2, 14, 4, 9, 5, 4, 4, 10, 4, 6, 8, 11, 4, 8, 3, 4, 8, 11, 4, 9, 5, 10, 4, 9, 8, 12, 6

Offset: 1

Author

Patrick De Geest, Oct 15 2000

Keywords

• nonn

Links

• Max Alekseyev, Table of n, a(n) for n = 1..583 (first 531 terms from Amiram Eldar)
• S. S. Wagstaff, Jr., The Cunningham Project

Crossrefs

bigomega(b^n+1): A057934 (b=10), A057935 (b=9), A057936 (b=8), A057937 (b=7), A057938 (b=6), A057939 (b=5), this sequence (b=4), A057941 (b=3), A054992 (b=2).

Cf. A001222, A052539, A057957, A274903.

Programs

Maple

with(numtheory); A057940:=n->bigomega(4^n + 1); seq(A057940(n), n=1..100); # Wesley Ivan Hurt, Jan 28 2014

Mathematica

Table[PrimeOmega[4^n + 1], {n, 100}] (* Wesley Ivan Hurt, Jan 28 2014 *)

Formula

a(n) = A057957(2n) - A057957(n). - T. D. Noe, Jun 19 2003

a(n) = Omega(4^n + 1) = A001222(A052539(n)). - Wesley Ivan Hurt, Jan 28 2014

a(n) = A054992(2*n). - Amiram Eldar, Feb 01 2020