a(n) has exactly (a(n) - n) / 2 partitions with exactly (a(n) - n) / 2 prime parts.

Terms

a(0) =2a(1) =5a(2) =8a(3) =13a(4) =20a(5) =29a(6) =42a(7) =57a(8) =78a(9) =109a(10) =148a(11) =197a(12) =264a(13) =347a(14) =454a(15) =595a(16) =770a(17) =989a(18) =1272a(19) =1619a(20) =2054a(21) =2601a(22) =3268a(23) =4087a(24) =5108a(25) =6347a(26) =7860a(27) =9713a(28) =11948a(29) =14653