a(n) = Sum_{k=1..n} k^3*sigma(k), where sigma is A000203.

Terms

a(0) =1a(1) =25a(2) =133a(3) =581a(4) =1331a(5) =3923a(6) =6667a(7) =14347a(8) =23824a(9) =41824a(10) =57796a(11) =106180a(12) =136938a(13) =202794a(14) =283794a(15) =410770a(16) =499204a(17) =726652a(18) =863832a(19) =1199832a(20) =1496184a(21) =1879512a(22) =2171520a(23) =3000960a(24) =3485335a(25) =4223527a(26) =5010847a(27) =6240159a(28) =6971829a(29) =8915829