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%I #5 May 08 2024 08:52:45
%S 1,1,1,2,3,5,7,10,13,18,21,29,31,46,43,65,61,91,77,128,95,172,127,213,
%T 149,292,181,347,231,437,259,562,289,679,361,772,431,991,467,1104,565,
%U 1352,605,1613,647,1877,835,2048,881,2529,965,2802,1135,3216,1187
%N a(1) = a(2) = 1; a(n+2) = Sum_{k=1..n} a(gcd(n,k)).
%F G.f. A(x) satisfies: A(x) = x + x^2 * ( 1 + Sum_{k>=1} phi(k) * A(x^k) ).
%F a(1) = a(2) = 1; a(n+2) = Sum_{d|n} phi(n/d) * a(d).
%t a[1] = a[2] = 1; a[n_] := a[n] = Sum[a[GCD[n - 2, k]], {k, 1, n - 2}]; Table[a[n], {n, 1, 55}]
%t nmax = 55; A[_] = 0; Do[A[x_] = x + x^2 (1 + Sum[EulerPhi[k] A[x^k], {k, 1, nmax}]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] // Rest
%Y Cf. A000010, A006874, A038045.
%K nonn
%O 1,4
%A _Ilya Gutkovskiy_, May 07 2024