A057941 - OEIS

%I #28 Jul 25 2023 19:29:39

%S 2,2,3,2,3,3,3,3,5,4,4,3,3,4,6,2,5,4,4,3,7,4,3,6,5,4,7,4,5,6,4,2,7,4,

%T 5,4,5,4,8,5,4,7,3,5,10,4,5,4,5,8,9,4,4,5,7,6,8,4,4,7,4,5,13,2,5,6,4,

%U 5,9,9,7,8,4,5,12,6,6,7,5,5,12,5,6,10,9,7,11,6,5,9,8,4,9,4,8,6,5,9,14,6,4

%N Number of prime factors of 3^n + 1 (counted with multiplicity).

%H Max Alekseyev, <a href="/A057941/b057941.txt">Table of n, a(n) for n = 1..691</a> (first 658 terms from Amiram Eldar)

%H S. S. Wagstaff, Jr., <a href="http://www.cerias.purdue.edu/homes/ssw/cun/index.html">The Cunningham Project</a>

%F a(n) = A057958(2n) - A057958(n) - _T. D. Noe_, Jun 19 2003

%F a(n) = A001222(A034472(n)). - _Amiram Eldar_, Feb 01 2020

%t PrimeOmega[3^Range[110]+1] (* _Harvey P. Dale_, Jun 20 2015 *)

%o (PARI) a(n)=bigomega(n^3+1) \\ _Charles R Greathouse IV_, Sep 14 2015

%Y bigomega(b^n+1): A057934 (b=10), A057935 (b=9), A057936 (b=8), A057937 (b=7), A057938 (b=6), A057939 (b=5), A057940 (b=4), this sequence (b=3), A054992 (b=2).

%Y Cf. A001222, A007658, A034472, A057958, A074476.

%K nonn

%O 1,1

%A _Patrick De Geest_, Oct 15 2000