a(n) = 1*t(n) + 2*t(n-1) + ... + k*t(n+1-k), where k=floor((n+1)/2) and t = A008578 ({1} U primes).

Terms

a(0) =1a(1) =2a(2) =7a(3) =11a(4) =26a(5) =40a(6) =76a(7) =104a(8) =171a(9) =219a(10) =331a(11) =397a(12) =566a(13) =672a(14) =912a(15) =1046a(16) =1369a(17) =1561a(18) =1985a(19) =2223a(20) =2762a(21) =3026a(22) =3688a(23) =4030a(24) =4833a(25) =5215a(26) =6179a(27) =6631a(28) =7764a(29) =8318