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

Terms

a(0) =3a(1) =6a(2) =10a(3) =14a(4) =20a(5) =24a(6) =30a(7) =34a(8) =41a(9) =46a(10) =54a(11) =59a(12) =70a(13) =76a(14) =82a(15) =88a(16) =96a(17) =102a(18) =110a(19) =115a(20) =124a(21) =131a(22) =139a(23) =147a(24) =156a(25) =162a(26) =170a(27) =179a(28) =192a(29) =197