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A068318
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Sum of prime factors of n-th semiprime.
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14
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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, 18, 43, 22, 45, 32, 20, 34, 49, 24, 55, 40, 28, 61, 24, 22, 63, 44, 46, 26, 69, 50, 73, 24, 34, 75, 36, 81, 56, 30, 85, 26, 62, 91, 64, 42, 28, 99, 70, 103, 36, 46, 105, 30, 74, 109
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OFFSET
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1,1
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COMMENTS
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a(n) = A003415(A001358(n)), the arithmetic derivative.
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
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
Robert G. Wilson v, Graph of n and a(n)
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FORMULA
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a(n) = A001414(A001358(n)).
If A001358(n)=s*p, then in this sequence a(n)=s+p.
a(n) = A084126(n)+A084127(n). - Reinhard Zumkeller, Jul 24 2006 [Typo in formula fixed by Zak Seidov, Aug 23 2014 ]
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EXAMPLE
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a(2)=5 because A001358(2)=6=2*3 and 2+3=5.
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MAPLE
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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
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MATHEMATICA
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f[n_] := Total[#1*#2 & @@@ FactorInteger@ n]; f@# & /@ Select[Range@300, PrimeOmega@# == 2 &] (* Robert G. Wilson v, Jan 23 2013 *)
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CROSSREFS
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Semiprimes are in A001358.
Cf. A120831, A120832, A120833, A120834, A109313.
Sequence in context: A143789 A068521 A196697 * A347932 A242337 A201739
Adjacent sequences: A068315 A068316 A068317 * A068319 A068320 A068321
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller, Feb 27 2002
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STATUS
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approved
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