A343930 -id:A343930 - cp's OEIS frontend

A343933 a(n) = (Sum_{k=1..n} (-k)^k) mod n.

0, 1, 0, 0, 2, 5, 6, 4, 8, 7, 0, 4, 10, 3, 10, 4, 12, 15, 3, 4, 3, 19, 2, 20, 11, 3, 23, 16, 15, 1, 11, 4, 1, 9, 24, 12, 1, 11, 36, 28, 26, 41, 5, 12, 20, 45, 26, 4, 5, 35, 16, 32, 48, 45, 23, 44, 51, 23, 3, 32, 29, 25, 44, 4, 24, 19, 64, 56, 28, 29, 44, 60, 54, 71, 12, 24, 51, 65, 55, 36, 68, 21, 1, 40, 38

Offset: 1

Seiichi Manyama, May 04 2021

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Cf. A341437, A343930, A343931.

a[n_] := Mod[Sum[PowerMod[-k, k, n], {k, 1, n}], n]; Array[a, 100] (* Amiram Eldar, May 04 2021 *)

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

A343931 Numbers k such that Sum_{j=1..k} (-j)^j == 0 (mod k).

Original entry on oeis.org

1, 3, 4, 11, 131, 188, 324, 445, 3548, 8284, 201403, 253731, 564084, 1812500, 4599115

Offset: 1

Seiichi Manyama, May 04 2021

Also numbers k such that k divides A001099(k).

Cf. A001099, A128981, A341437, A343930, A343933.

q[n_] := Divisible[Sum[PowerMod[-k, k, n], {k, 1, n}], n]; Select[Range[8500], q] (* Amiram Eldar, May 04 2021 *)

isok(n) = sum(k=1, n, Mod(-k, n)^k)==0;

from itertools import accumulate, count, islice
def A343931_gen(): # generator of terms
    yield 1
    for i, j in enumerate(accumulate((-k)**k for k in count(1)),start=2):
        if j % i == 0:
            yield i
A343931_list = list(islice(A343931_gen(),10)) # Chai Wah Wu, Jun 18 2022

a(11)-a(13) from Chai Wah Wu, May 04 2021
a(14) from Martin Ehrenstein, May 05 2021
a(15) from Martin Ehrenstein, May 08 2021

cp's OEIS Frontend

A343933 a(n) = (Sum_{k=1..n} (-k)^k) mod n.

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