A341036 -id:A341036 - cp's OEIS frontend

A342449 a(n) = Sum_{k=1..n} gcd(k,n)^k.

1, 5, 29, 262, 3129, 46705, 823549, 16777544, 387421251, 10000003469, 285311670621, 8916100581446, 302875106592265, 11112006826387025, 437893890391180013, 18446744073743123788, 827240261886336764193, 39346408075299116257065

Offset: 1

Seiichi Manyama, Mar 13 2021

nonn

Cf. A000010, A001923, A018804, A050873, A231712, A332517, A341036, A342370, A342389, A342423.

a[n_] := Sum[GCD[k, n]^k, {k, 1, n}]; Array[a, 20] (* Amiram Eldar, Mar 13 2021 *)

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

If p is prime, a(p) = p-1 + p^p = A231712(p).

A342370 a(n) = Sum_{k=1..n} gcd(k,n)^(k-1).

Original entry on oeis.org

1, 3, 11, 68, 629, 7797, 117655, 2097254, 43046979, 1000000799, 25937424611, 743008402000, 23298085122493, 793714773374529, 29192926027528343, 1152921504613147242, 48661191875666868497, 2185911559739107208115, 104127350297911241532859, 5242880000000008181608132

Offset: 1

Seiichi Manyama, Mar 13 2021

nonn

Martin Ehrenstein, Table of n, a(n) for n = 1..400

Cf. A000010, A018804, A056665, A173235, A341036, A342394, A342433, A342436, A342449.

a[n_] := Sum[GCD[k, n]^(k - 1), {k, 1, n}]; Array[a, 20] (* Amiram Eldar, Mar 13 2021 *)

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

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

a(19) and beyond from Martin Ehrenstein, Mar 13 2021

cp's OEIS Frontend

A342449 a(n) = Sum_{k=1..n} gcd(k,n)^k.

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