A342449 -id:A342449 - cp's OEIS frontend

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

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

A341036 a(n) = Sum_{k=1..n} gcd(k,n)^(k-2).

Original entry on oeis.org

1, 2, 5, 19, 129, 1306, 16813, 262181, 4783059, 100000214, 2357947701, 61917372083, 1792160394049, 56693912393474, 1946195068811453, 72057594039243049, 2862423051509815809, 121439531096661117354, 5480386857784802185957

Offset: 1

Seiichi Manyama, Mar 13 2021

nonn

Cf. A000010, A018804, A342370, A342432, A342449.

a[n_] := Sum[GCD[k, n]^(k - 2), {k, 1, n}]; Array[a, 20] (* Amiram Eldar, Mar 13 2021 *)

PARI
```
a(n) = sum(k=1, n, gcd(k, n)^(k-2));
```

A343114 a(n) = Sum_{i=1..n} gcd(n^i,i).

Original entry on oeis.org

1, 3, 5, 8, 9, 17, 13, 20, 21, 35, 21, 50, 25, 49, 51, 48, 33, 91, 37, 88, 77, 89, 45, 126, 65, 107, 81, 124, 57, 255, 61, 112, 141, 163, 137, 242, 73, 177, 167, 232, 81, 365, 85, 220, 227, 209, 93, 328, 133, 315, 213, 264, 105, 393, 229, 342, 257, 267, 117, 680, 121, 281

Offset: 1

Wesley Ivan Hurt, Apr 05 2021

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..1000

Cf. A018804 (Pillai's function), A342449.

Table[Sum[GCD[n^i, i], {i, n}], {n, 100}]

a(n) = sum(i=1, n, gcd(n^i, i)); \\ Michel Marcus, Apr 05 2021

If p is prime, a(p) = 2*p -1. - Seiichi Manyama, Apr 06 2021

A343395 a(n) = Sum_{i=1..n} gcd(n^(n-i),n-i).

Original entry on oeis.org

1, 2, 3, 5, 5, 12, 7, 13, 13, 26, 11, 39, 13, 36, 37, 33, 17, 74, 19, 69, 57, 68, 23, 103, 41, 82, 55, 97, 29, 226, 31, 81, 109, 130, 103, 207, 37, 140, 129, 193, 41, 324, 43, 177, 183, 164, 47, 281, 85, 266, 163, 213, 53, 340, 175, 287, 201, 210, 59, 621, 61, 220, 289

Offset: 1

Wesley Ivan Hurt, Apr 13 2021

nonn

Cf. A018804 (Pillai's function), A342449, A343114.

Table[Sum[GCD[n^(n - i), n - i], {i, n}], {n, 100}]

a(n) = sum(i=1, n, gcd(n^(n-i), n-i)); \\ Michel Marcus, Apr 15 2021

cp's OEIS Frontend

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

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A341036 a(n) = Sum_{k=1..n} gcd(k,n)^(k-2).

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A343114 a(n) = Sum_{i=1..n} gcd(n^i,i).

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Formula

A343395 a(n) = Sum_{i=1..n} gcd(n^(n-i),n-i).

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Mathematica

PARI