a(n) = n + Sum_{k=1..n} pi(k), where pi() = A000720.

Terms

a(0) =0a(1) =1a(2) =3a(3) =6a(4) =9a(5) =13a(6) =17a(7) =22a(8) =27a(9) =32a(10) =37a(11) =43a(12) =49a(13) =56a(14) =63a(15) =70a(16) =77a(17) =85a(18) =93a(19) =102a(20) =111a(21) =120a(22) =129a(23) =139a(24) =149a(25) =159a(26) =169a(27) =179a(28) =189a(29) =200