a(n) = Sum_{d|n} p(d), where p(d) = A000041 = number of partitions of d.

Terms

a(0) =1a(1) =3a(2) =4a(3) =8a(4) =8a(5) =17a(6) =16a(7) =30a(8) =34a(9) =52a(10) =57a(11) =99a(12) =102a(13) =153a(14) =187a(15) =261a(16) =298a(17) =432a(18) =491a(19) =684a(20) =811a(21) =1061a(22) =1256a(23) =1696a(24) =1966a(25) =2540a(26) =3044a(27) =3876a(28) =4566a(29) =5846