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Search: id:A090967
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| A090967 |
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Given the sequence of the sums of the divisors of the semiprimes, this is the subsequence where each sum is an even number. |
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+0
3
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| 4, 6, 8, 10, 10, 14, 12, 16, 14, 20, 16, 22, 18, 26, 18, 22, 32, 20, 34, 24, 40, 28, 24, 22, 44, 46, 26, 50, 24, 34, 36, 56, 30, 26, 62, 64, 42, 28, 70, 36, 46, 30, 74, 48, 38, 76, 30, 52, 82, 32, 86, 34, 44, 58, 92, 48, 34, 100, 64, 36, 50, 104, 66, 106
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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This is the sequence of the sums of the divisors of the n-th semiprime, with all the odd entries removed. Goldbach's Conjecture states that this sequence will include all even integers greater than or equal to 4. This sequence is in some ways the order in which Goldbach's Conjecture is satisfied.
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EXAMPLE
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a(7)=12 since the seventh semiprime whose two factors sum to an even number is 35, since 35=5*7 and 5+7=12.
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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}]; GenerateA090967[n_] := Select[SumOfFactorsOfSemiprimes[n], Mod[ #, 2] == 0 &]; GenerateA090967[100] would give the first 100 terms of the sequence.
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CROSSREFS
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Cf. A001358, A068318.
Sequence in context: A087789 A071830 A020891 this_sequence A075254 A139203 A061408
Adjacent sequences: A090964 A090965 A090966 this_sequence A090968 A090969 A090970
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KEYWORD
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nonn
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AUTHOR
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Ryan Witko (witko(AT)nyu.edu), Feb 27 2004
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