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a(n) = sum of exponents in prime-power factorization of 2*prime(n)+1.
2

%I #11 Oct 02 2017 20:22:02

%S 1,1,1,2,1,3,2,2,1,1,3,3,1,2,2,1,2,2,4,2,3,2,1,1,3,2,3,2,2,1,3,1,3,3,

%T 2,2,4,2,2,1,1,3,1,3,2,3,3,2,3,4,1,1,3,1,2,2,3,2,3,1,5,1,3,2,3,2,3,5,

%U 2,2,2,1,4,3,3,2,2,3,2,4,1,2,1,3,2,1,2,3,2,3,3,2,4,1,4,2,1,2,2

%N a(n) = sum of exponents in prime-power factorization of 2*prime(n)+1.

%t Array[Plus@@Last/@FactorInteger[2*Prime[ # ]+1]&,6! ] (* _Vladimir Joseph Stephan Orlovsky_, Feb 28 2010 *)

%t Total[FactorInteger[#][[All,2]]]&/@(2*Prime[Range[100]]+1) (* _Harvey P. Dale_, Oct 02 2017 *)

%K nonn

%O 1,4

%A _Clark Kimberling_