a(n) = Sum_{k=1..n} d(k)*prime(k), where d(k) = A001223.

Terms

a(0) =2a(1) =8a(2) =18a(3) =46a(4) =68a(5) =120a(6) =154a(7) =230a(8) =368a(9) =426a(10) =612a(11) =760a(12) =842a(13) =1014a(14) =1296a(15) =1614a(16) =1732a(17) =2098a(18) =2366a(19) =2508a(20) =2946a(21) =3262a(22) =3760a(23) =4472a(24) =4860a(25) =5062a(26) =5474a(27) =5688a(28) =6124a(29) =7706