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a(n) is the number of distinct prime divisors of 2*prime(n)+1.
4

%I #9 Jul 09 2022 15:36:07

%S 1,1,1,2,1,1,2,2,1,1,2,2,1,2,2,1,2,2,2,2,2,2,1,1,3,2,2,2,2,1,3,1,2,2,

%T 2,2,3,2,2,1,1,2,1,2,2,3,2,2,3,2,1,1,3,1,2,2,2,2,3,1,2,1,3,2,3,2,3,2,

%U 2,2,2,1,3,2,3,2,2,3,2,3,1,2,1,2,2,1,2,3,2,2,3,2,3,1,2,2,1,2,2

%N a(n) is the number of distinct prime divisors of 2*prime(n)+1.

%H Michael De Vlieger, <a href="/A023589/b023589.txt">Table of n, a(n) for n = 1..10000</a>

%t Array[PrimeNu[2 Prime[#] + 1] &, 99] (* _Michael De Vlieger_, Jul 09 2022 *)

%o (PARI) a(n) = omega(2*prime(n)+1) \\ _Hugo Pfoertner_, Jul 09 2022

%Y Cf. A001221, A072055.

%K nonn

%O 1,4

%A _Clark Kimberling_