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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

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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));