a(n) = 2^n - Sum_{m=0..n} binomial(n/gcd(n,m), m/gcd(n,m)) = 2^n - A082906.

Terms

a(0) =0a(1) =0a(2) =0a(3) =4a(4) =0a(5) =42a(6) =0a(7) =116a(8) =162a(9) =730a(10) =0a(11) =2458a(12) =0a(13) =11494a(14) =16890a(15) =32628a(16) =0a(17) =180960a(18) =0a(19) =554994a(20) =931476a(21) =2800534a(22) =0a(23) =11005898a(24) =6643750a(25) =43946838a(26) =44738892a(27) =136580910a(28) =0a(29) =720879712