a(n) = Sum_{k=1..n-1} k^2*phi(k) + n^2*phi(n)/2, where phi = A000010.

Terms

a(0) =3a(1) =14a(2) =39a(3) =105a(4) =191a(5) =374a(6) =649a(7) =1020a(8) =1463a(9) =2268a(10) =3161a(11) =4463a(12) =6065a(13) =7553a(14) =9477a(15) =12813a(16) =16097a(17) =20318a(18) =25167a(19) =29413a(20) =34479a(21) =42718a(22) =50841a(23) =59395a(24) =69701a(25) =80318a(26) =91583a(27) =108061a(28) =123435a(29) =141450