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a(1) = 1; a(n) = n * Sum_{d|n, d < n, gcd(d, n/d) = 1} a(d) / d.
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%I #10 Mar 06 2020 22:41:12

%S 1,2,3,4,5,18,7,8,9,30,11,36,13,42,45,16,17,54,19,60,63,66,23,72,25,

%T 78,27,84,29,390,31,32,99,102,105,108,37,114,117,120,41,546,43,132,

%U 135,138,47,144,49,150,153,156,53,162,165,168,171,174,59,780,61,186,189,64,195

%N a(1) = 1; a(n) = n * Sum_{d|n, d < n, gcd(d, n/d) = 1} a(d) / d.

%t a[1] = 1; a[n_] := a[n] = n Sum[If[GCD[d, n/d] == 1 && d < n, a[d]/d, 0], {d, Divisors[n]}]; Table[a[n], {n, 1, 65}]

%Y Cf. A000961 (fixed points), A050369, A325446.

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, Mar 06 2020