A343492 - OEIS

%I #11 Apr 17 2021 08:13:05

%S 1,6,27,132,629,3162,15631,78264,390681,1953774,9765635,48831564,

%T 244140637,1220718786,6103516983,30517656528,152587890641,

%U 762939850086,3814697265643,19073488283028,95367431672037,476837167968810,2384185791015647,11920929004069128

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

%F a(n) = Sum_{d|n} phi(n/d)*5^(d - 1) = A054612(n)/5.

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

%t a[n_] := Sum[5^(GCD[k, n] - 1), {k, 1, n}]; Array[a, 24] (* _Amiram Eldar_, Apr 17 2021 *)

%o (PARI) a(n) = sum(k=1, n, 5^(gcd(k, n)-1));

%o (PARI) a(n) = sumdiv(n, d, eulerphi(n/d)*5^(d-1));

%o (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, eulerphi(k)*x^k/(1-5*x^k)))

%Y Column 5 of A343489.

%Y Cf. A000010, A054612.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Apr 17 2021