

A090967


Given the sequence of the sums of the divisors of the semiprimes, this is the subsequence where each sum is an even number.


3



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
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OFFSET

1,1


COMMENTS

This is the sequence of the sums of the divisors of the nth 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.


LINKS



EXAMPLE

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.


MATHEMATICA

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.


CROSSREFS



KEYWORD

nonn


AUTHOR

Ryan Witko (witko(AT)nyu.edu), Feb 27 2004


STATUS

approved



