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

Terms

a(0) =1a(1) =5a(2) =10a(3) =25a(4) =36a(5) =80a(6) =106a(7) =201a(8) =280a(9) =460a(10) =617a(11) =1024a(12) =1314a(13) =2000a(14) =2685a(15) =3897a(16) =5050a(17) =7280a(18) =9311a(19) =13020a(20) =16747a(21) =22665a(22) =28866a(23) =39000a(24) =48986a(25) =64654a(26) =81550a(27) =106124a(28) =132386a(29) =171295