a(n) = Sum_{k = 1..n} k*floor((n + prime(k))/k).

Terms

a(0) =3a(1) =8a(2) =17a(3) =29a(4) =51a(5) =70a(6) =97a(7) =122a(8) =161a(9) =195a(10) =254a(11) =303a(12) =393a(13) =455a(14) =518a(15) =586a(16) =667a(17) =747a(18) =834a(19) =915a(20) =1024a(21) =1125a(22) =1238a(23) =1364a(24) =1481a(25) =1603a(26) =1744a(27) =1919a(28) =2125a(29) =2246