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%I #30 May 26 2021 13:47:51
%S 4,5,6,7,9,8,10,13,10,15,14,19,12,21,16,25,14,20,16,22,31,33,18,26,39,
%T 18,43,22,45,32,20,34,49,24,55,40,28,61,24,22,63,44,46,26,69,50,73,24,
%U 34,75,36,81,56,30,85,26,62,91,64,42,28,99,70,103,36,46,105,30,74,109
%N Sum of prime factors of n-th semiprime.
%C a(n) = A003415(A001358(n)), the arithmetic derivative.
%C Odd k is a term if and only if k - 2 is prime. Goldbach's conjecture implies that every even number k >= 4 is a term. - _Jianing Song_, May 26 2021
%H T. D. Noe, <a href="/A068318/b068318.txt">Table of n, a(n) for n=1..1000</a>
%H Robert G. Wilson v, <a href="/A068318/a068318.pdf">Graph of n and a(n)</a>
%F a(n) = A001414(A001358(n)).
%F If A001358(n)=s*p, then in this sequence a(n)=s+p.
%F a(n) = A084126(n)+A084127(n). - _Reinhard Zumkeller_, Jul 24 2006 [Typo in formula fixed by _Zak Seidov_, Aug 23 2014 ]
%e a(2)=5 because A001358(2)=6=2*3 and 2+3=5.
%p with(numtheory): a:=proc(n) if bigomega(n)=2 and nops(factorset(n))=2 then factorset(n)[1]+factorset(n)[2] elif bigomega(n)=2 then 2*sqrt(n) else fi end: seq(a(n),n=1..214); # _Emeric Deutsch_
%t f[n_] := Total[#1*#2 & @@@ FactorInteger@ n]; f@# & /@ Select[Range@300, PrimeOmega@# == 2 &] (* _Robert G. Wilson v_, Jan 23 2013 *)
%Y Semiprimes are in A001358.
%Y Cf. A120831, A120832, A120833, A120834, A109313.
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Feb 27 2002
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