a(n) = Sum_{k=1..n} tau(gcd(k,n))^(n/gcd(k,n)), where tau(n) is the number of divisors of n.

Terms

a(0) =1a(1) =3a(2) =4a(3) =9a(4) =6a(5) =26a(6) =8a(7) =49a(8) =25a(9) =140a(10) =12a(11) =240a(12) =14a(13) =782a(14) =156a(15) =1215a(16) =18a(17) =3349a(18) =20a(19) =5130a(20) =800a(21) =20498a(22) =24a(23) =19558a(24) =151a(25) =98324a(26) =3148a(27) =111492a(28) =30a(29) =270624