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

Terms

a(0) =1a(1) =5a(2) =29a(3) =262a(4) =3129a(5) =46705a(6) =823549a(7) =16777544a(8) =387421251a(9) =10000003469a(10) =285311670621