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Largest term is 60060 (see b-file). No more terms < 10^8. Conjectured to be complete.
Donovan Johnson, Table of n, a(n) for n=2..196
20 is in this sequence because no 4-almost prime and a prime sum to 20. 21 is not in this sequence because the sum of 16 (4-almost prime) and 5 (prime) is 21.
Cf. A000040, A014613, A130588, A146296, A146297.
Sequence in context: A247752 A275156 A188459 * A123719 A113221 A113219
Adjacent sequences: A146292 A146293 A146294 * A146296 A146297 A146298
Donovan Johnson, Nov 05 2008