A342437 a(n) = Sum_{k=1..n} gcd(k,n)^(n/gcd(k,n) - 1).

1, 2, 3, 5, 5, 14, 7, 25, 25, 74, 11, 161, 13, 398, 383, 657, 17, 2110, 19, 3341, 4485, 10262, 23, 19569, 2521, 49178, 39547, 74441, 29, 221462, 31, 328737, 590753, 1048610, 103379, 1905565, 37, 4718630, 6377655, 5573801, 41, 22462826, 43, 31459985, 40634221, 92274734, 47

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..5000

Formula

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

If p is prime, a(p) = p.

Mathematica

a[n_] := Sum[GCD[k, n]^(n/GCD[k, n] - 1), {k, 1, n}]; Array[a, 50] (* Amiram Eldar, Mar 12 2021 *)

Prog

(PARI) a(n) = sum(k=1, n, gcd(k, n)^(n/gcd(k, n)-1));
(PARI) a(n) = sumdiv(n, d, eulerphi(n/d)*d^(n/d-1));

Crossrefs

Cf. A000010, A226459, A342421, A342424.

Sequence in context: A097453 A079125 A146305 * A079022 A368706 A368674

Adjacent sequences: A342434 A342435 A342436 * A342438 A342439 A342440

Keyword

nonn

Author

Seiichi Manyama, Mar 12 2021

Status

approved