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A090967 Given the sequence of the sums of the divisors of the semiprimes, this is the subsequence where each sum is an even number. 2
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; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..64.

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

Cf. A001358, A068318.

Sequence in context: A276982 A167146 A020891 * A272475 A184016 A075254

Adjacent sequences:  A090964 A090965 A090966 * A090968 A090969 A090970

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified October 15 10:15 EDT 2019. Contains 328026 sequences. (Running on oeis4.)