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Search: id:A068318
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| A068318 |
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Sum of prime factors of n-th semiprime. |
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+0
11
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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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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a(n) = A003415(A001358(n)), the arithmetic derivative.
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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 (reinhard.zumkeller(AT)lhsystems.com), Jul 24 2006
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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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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.
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CROSSREFS
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Semiprimes are in A001358.
Cf. A120831, A120832, A120833, A120834.
Sequence in context: A140293 A075341 A068521 this_sequence A066485 A079445 A120173
Adjacent sequences: A068315 A068316 A068317 this_sequence A068319 A068320 A068321
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Feb 27 2002
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