Let p(k) be the number of partitions of k (A000041); a(n) = Sum_{1<=k<=n, gcd(k,n)=1} p(k).

Terms

a(0) =1a(1) =1a(2) =3a(3) =4a(4) =11a(5) =8a(6) =29a(7) =26a(8) =52a(9) =49a(10) =138a(11) =79a(12) =271a(13) =198a(14) =337a(15) =389a(16) =914a(17) =477a(18) =1596a(19) =993a(20) =1881a(21) =1912a(22) =4507a(23) =2222a(24) =6485a(25) =5080a(26) =8682a(27) =7384a(28) =18459a(29) =6780