Search: id:A068318
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%I A068318
%S A068318 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 A068318 18,43,22,45,32,20,34,49,24,55,40,28,61,24,22,63,44,46,26,69,50,73,24,
%U A068318 34,75,36,81,56,30,85,26,62,91,64,42,28,99,70,103,36,46,105,30,74,109
%N A068318 Sum of prime factors of n-th semiprime.
%C A068318 a(n) = A003415(A001358(n)), the arithmetic derivative.
%H A068318 T. D. Noe, <a href="b068318.txt">Table of n, a(n) for n=1..1000</a>
%F A068318 a(n) = A001414(A001358(n)).
%F A068318 If A001358(n)=s*p, then in this sequence a(n)=s+p
%F A068318 a(n) = A084126(n)*A084127(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Jul 24 2006
%e A068318 a(2)=5 because A001358(2)=6=2*3 and 2+3=5
%p A068318 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 A068318 PrimeFactorExponentsAdded[n_] := Plus @@ Flatten[Table[ #[[2]], {1}] 
               & /@ FactorInteger[n]]; PrimeFactorsAdded[n_] := Plus @@ Flatten[Table[ 
               #[[1]]*#[[2]], {1}] & /@ FactorInteger[n]]; SumOfFactorsOfSemiprimes[n_] 
               := Table[PrimeFactorsAdded[Part[Select[ Range[n*n], PrimeFactorExponentsAdded[ 
               # ] == 2 &], a]], {a, 1, n}]; SumOfFactorsOfSemiprimes[100] gives 
               the first 100 terms in the sequence.
%Y A068318 Semiprimes are in A001358.
%Y A068318 Cf. A120831, A120832, A120833, A120834.
%Y A068318 Sequence in context: A075341 A143789 A068521 this_sequence A066485 A079445 
               A120173
%Y A068318 Adjacent sequences: A068315 A068316 A068317 this_sequence A068319 A068320 
               A068321
%K A068318 nonn
%O A068318 1,1
%A A068318 Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 27 2002

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