a(n) = Sum_{k=1..n} k^3*sigma_2(k), where sigma_2 is A001157.

Terms

a(0) =1a(1) =41a(2) =311a(3) =1655a(4) =4905a(5) =15705a(6) =32855a(7) =76375a(8) =142714a(9) =272714a(10) =435096a(11) =797976a(12) =1171466a(13) =1857466a(14) =2734966a(15) =4131702a(16) =5556472a(17) =8210032a(18) =10692990a(19) =15060990a(20) =19691490a(21) =26186770a(22) =32635280a(23) =44385680a(24) =54557555a(25) =69497155a(26) =85637215a(27) =108686815a(28) =129222353a(29) =164322353