a(n) = Sum_{k=1..n} n^(k/gcd(n, k)).

Terms

a(0) =1a(1) =4a(2) =15a(3) =76a(4) =785a(5) =7836a(6) =137263a(7) =2130976a(8) =47895489a(9) =1010012140a(10) =28531167071a(11) =743044702104