cp's OEIS Frontend

A110874 Number of prime factors of 2 + n^(n+1) counted with multiplicity.

%I A110874 #16 Sep 17 2023 15:40:39
%S A110874 1,2,1,5,2,2,4,5,2,5,4,4,5,3,1,4,5,3,4,6,3,8,4,5,4,4,2,6,3,6,5,5,5,6,
%T A110874 6,8,6,6,4,5,4,6,4,5,3,8,4,3,5,5,5,7,7,11,4,5,4,13,4,6,2,5,2,6,6,5,8,
%U A110874 9,5,9,4,7,4,4,5,7,6,7,6,9,4,9,5,8,5,8
%N A110874 Number of prime factors of 2 + n^(n+1) counted with multiplicity.
%C A110874 Compared with A110676, number of prime factors with multiplicity of 2 + n^(n+1), this seems to have an unlimited number of primes (n = 1, 3, 15, ...) and semiprimes (n = 2, 5, 6, 9, 27, ...). Of course, n even gives n | a(n).
%H A110874 Sean A. Irvine, <a href="/A110874/b110874.txt">Table of n, a(n) for n = 1..100</a>
%F A110874 a(n) = A001222(1 + A110567(n)) = A001222(2 + A007778(n)) = A001222(2 + n^(n+1)).
%e A110874 a(1) = 1 because 2 + 1^2 = 3 is prime (one prime factor).
%e A110874 a(2) = 2 because 2 + 2^3 = 10 = 2 * 5 is semiprime (two prime factors).
%e A110874 a(3) = 1 because 2 + 3^4 = 83 is prime.
%e A110874 a(4) = 5 because 2 + 4^5 = 1026 = 2 * 3^3 * 19 has five prime factors (3 has multiplicity of 3).
%e A110874 a(5) = 2 because 2 + 5^6 = 15627 = 3 * 5209 is semiprime (two prime factors).
%e A110874 a(6) = 2 because 2 + 6^7 = 279938 = 2 * 139969 is semiprime (two prime factors).
%e A110874 a(15) = 1 because 2 + 15^16 = 6568408355712890627 is prime. What is the next prime?
%t A110874 Table[PrimeOmega[2+n^(n+1)],{n,41}] (* _Harvey P. Dale_, Nov 08 2020 *)
%Y A110874 Cf. A001222, A007778, A110567, A110676.
%K A110874 nonn
%O A110874 1,2
%A A110874 _Jonathan Vos Post_, Sep 18 2005
%E A110874 More terms from _Sean A. Irvine_, Sep 17 2023