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%I #12 Oct 17 2017 09:28:53
%S 3,5,7,11,13,17,19,25,29,33,35,41,43,47,51,59,61,67,69,75,79,83,85,93,
%T 97,101,107,113,115,121,123,133,137,141,145,153,155,159,163,171,173,
%U 179,181,187,193,197,199,209,213,219,223,229,231,239,243,251,255,259,261
%N Recursive sum of 2*Omega(n), where Omega(n) is the sequence A001222.
%C Note that the first 7 terms are prime numbers. See also the sum of Omega (A022559).
%H G. C. Greubel, <a href="/A123567/b123567.txt">Table of n, a(n) for n = 1..5000</a>
%F a(n+1) = a(n) + 2*A001222(n), with a(1)=3.
%e a(2)=a(1)+2*Omega(1)=3+2=5;
%e a(3)=a(2)+2*Omega(2)=5+2=7;
%e a(4)=a(3)+2*Omega(3)=7+4=11;
%t Omega = Plus @@ Sum[Transpose[FactorInteger[ # ]][[2]]] &; FoldList[Plus, 3, 2Map[Omega, Range[2, 200]]]
%t nxt[{n_,a_}]:={n+1,a+2PrimeOmega[n]}; Rest[Transpose[NestList[nxt,{1,3}, 60]][[2]]] (* _Harvey P. Dale_, Mar 13 2016 *)
%t Fold[Append[#1, Last[#1] + 2 PrimeOmega[#2]] &, {3}, Range[2, 59]] (* _Michael De Vlieger_, Oct 16 2017 *)
%K nonn
%O 1,1
%A _Carlos Alves_, Nov 12 2006
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