A090967 Given the sequence of the sums of the divisors of the semiprimes, this is the subsequence where each sum is an even number.

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

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: A167146 A020891 A340848 * A349707 A272475 A184016

Adjacent sequences: A090964 A090965 A090966 * A090968 A090969 A090970

Keyword

nonn

Author

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

Status

approved