|
%I #1 Jun 12 2004 03:00:00
%S 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 44,46,26,50,24,34,36,56,30,26,62,64,42,28,70,36,46,30,74,48,38,76,30,
%U 52,82,32,86,34,44,58,92,48,34,100,64,36,50,104,66,106
%N Given the sequence of the sums of the divisors of the semiprimes, this is the subsequence where each sum is an even number.
%C 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 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 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.
%Y Cf. A001358, A068318.
%K nonn
%O 1,1
%A Ryan Witko (witko(AT)nyu.edu), Feb 27 2004
|
