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

1, 6, 27, 132, 629, 3162, 15631, 78264, 390681, 1953774, 9765635, 48831564, 244140637, 1220718786, 6103516983, 30517656528, 152587890641, 762939850086, 3814697265643, 19073488283028, 95367431672037, 476837167968810, 2384185791015647, 11920929004069128

Offset: 1

Author

Seiichi Manyama, Apr 17 2021

Keywords

• nonn

Crossrefs

Column 5 of A343489.

Cf. A000010, A054612.

Programs

Mathematica

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

PARI

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

PARI

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

PARI

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

Formula

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

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