This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A090967 #4 Aug 05 2025 21:30:34
%S A090967 4,6,8,10,10,14,12,16,14,20,16,22,18,26,18,22,32,20,34,24,40,28,24,22,
%T A090967 44,46,26,50,24,34,36,56,30,26,62,64,42,28,70,36,46,30,74,48,38,76,30,
%U A090967 52,82,32,86,34,44,58,92,48,34,100,64,36,50,104,66,106
%N A090967 Given the sequence of the sums of the divisors of the semiprimes, this is the subsequence where each sum is an even number.
%C A090967 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.
%e A090967 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.
%t A090967 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]
%Y A090967 Cf. A001358, A068318.
%K A090967 nonn
%O A090967 1,1
%A A090967 Ryan Witko (witko(AT)nyu.edu), Feb 27 2004