%I #6 Apr 16 2021 15:42:16

%S 5,-10,45,-160,629,-2590,11165,-48910,217045,-976258,4438925,

%T -20346440,93900245,-435959830,2034505661,-9536767660,44878791365,

%U -211927519090,1003867701485,-4768372070128,22706531350485,-108372079190350,518301258916445,-2483526875847690,11920928955078629

%N a(n) = -(1/n) * Sum_{d|n} phi(n/d) * (-5)^d.

%F G.f.: Sum_{k>=1} phi(k) * log(1 + 5*x^k) / k.

%F a(n) = -(1/n) * Sum_{k=1..n} (-5)^gcd(n,k).

%F Product_{n>=1} 1 / (1 - x^n)^a(n) = g.f. for A261569.

%t Table[-(1/n) Sum[EulerPhi[n/d] (-5)^d, {d, Divisors[n]}], {n, 1, 25}]

%t nmax = 25; CoefficientList[Series[Sum[EulerPhi[k] Log[1 + 5 x^k]/k, {k, 1, nmax}], {x, 0, nmax}], x] // Rest

%Y Cf. A000010, A001869, A038066, A074763, A261569, A343465, A343466.

%K sign

%O 1,1

%A _Ilya Gutkovskiy_, Apr 16 2021