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A343492 a(n) = Sum_{k=1..n} 5^(gcd(k, n) - 1).

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%I A343492 #11 Apr 17 2021 08:13:05
%S A343492 1,6,27,132,629,3162,15631,78264,390681,1953774,9765635,48831564,
%T A343492 244140637,1220718786,6103516983,30517656528,152587890641,
%U A343492 762939850086,3814697265643,19073488283028,95367431672037,476837167968810,2384185791015647,11920929004069128
%N A343492 a(n) = Sum_{k=1..n} 5^(gcd(k, n) - 1).
%F A343492 a(n) = Sum_{d|n} phi(n/d)*5^(d - 1) = A054612(n)/5.
%F A343492 G.f.: Sum_{k>=1} phi(k) * x^k / (1 - 5*x^k).
%t A343492 a[n_] := Sum[5^(GCD[k, n] - 1), {k, 1, n}]; Array[a, 24] (* _Amiram Eldar_, Apr 17 2021 *)
%o A343492 (PARI) a(n) = sum(k=1, n, 5^(gcd(k, n)-1));
%o A343492 (PARI) a(n) = sumdiv(n, d, eulerphi(n/d)*5^(d-1));
%o A343492 (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, eulerphi(k)*x^k/(1-5*x^k)))
%Y A343492 Column 5 of A343489.
%Y A343492 Cf. A000010, A054612.
%K A343492 nonn
%O A343492 1,2
%A A343492 _Seiichi Manyama_, Apr 17 2021