A342422 a(n) = Sum_{k=1..n} (n/gcd(k,n))^gcd(k,n).

1, 3, 7, 13, 21, 39, 43, 81, 109, 173, 111, 475, 157, 507, 1107, 1153, 273, 2997, 343, 6133, 6685, 3479, 507, 30819, 13001, 10533, 44227, 65071, 813, 234959, 931, 215553, 368265, 136241, 414183, 1991281, 1333, 531471, 3215947, 4883141, 1641, 12951117, 1807, 12735043, 36892689, 8401259

Offset: 1

Author

Seiichi Manyama, Mar 11 2021

Keywords

• nonn

Links

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

Crossrefs

Cf. A000010, A342421.

Programs

Mathematica

a[n_] := Sum[(n/GCD[k, n])^GCD[k, n], {k, 1, n}]; Array[a, 50] (* Amiram Eldar, Mar 11 2021 *)

PARI

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

PARI

a(n) = sumdiv(n, d, eulerphi(d^(n/d+1)));

PARI

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

Formula

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