A342396 -id:A342396 - cp's OEIS frontend

A342394 a(n) = Sum_{k=1..n} k^(gcd(k,n) - 1).

1, 3, 11, 68, 629, 7793, 117655, 2097228, 43046772, 1000000649, 25937424611, 743008379146, 23298085122493, 793714773371841, 29192926025401528, 1152921504608945960, 48661191875666868497, 2185911559738739835591, 104127350297911241532859

Offset: 1

Seiichi Manyama, Mar 10 2021

Cf. A056665, A173235, A342389, A342396.

a[n_] := Sum[k^(GCD[k, n] - 1), {k, 1, n}]; Array[a, 19] (* Amiram Eldar, Mar 10 2021 *)

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

If p is prime, a(p) = p-1 + p^(p-1) = A173235(p) = A056665(p).

A342395 a(n) = Sum_{k=1..n} k^(n/gcd(k,n)).

Original entry on oeis.org

1, 3, 12, 90, 1305, 15713, 376768, 6163324, 176787369, 3769360335, 142364319636, 3152514811878, 154718778284161, 4340009168261557, 210971169749009040, 7281661102087491416, 435659030617933827153, 14181101408651996188995

Offset: 1

Seiichi Manyama, Mar 10 2021

Cf. A121706, A332620, A342389, A342396.

a[n_] := Sum[k^(n/GCD[k, n]), {k, 1, n}]; Array[a, 18] (* Amiram Eldar, Mar 10 2021 *)

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

If p is prime, a(p) = A121706(p) + p.

cp's OEIS Frontend

A342394 a(n) = Sum_{k=1..n} k^(gcd(k,n) - 1).

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