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

1,2

Links

Table of n, a(n) for n=1..24.

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).

Mathematica

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

Prog

(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)))

Crossrefs

Column 5 of A343489.

Cf. A000010, A054612.

Sequence in context: A104745 A184279 A299598 * A323928 A360082 A174634

Adjacent sequences: A343489 A343490 A343491 * A343493 A343494 A343495

Keyword

nonn

Author

Seiichi Manyama, Apr 17 2021

Status

approved