A343933 -id:A343933 - cp's OEIS frontend

A343930 Numbers k such that Sum_{j=1..k} (-j)^j == 1 (mod k).

1, 2, 30, 33, 37, 83, 149, 262, 4030, 31969, 140225, 182730, 724754, 2337094, 3985753, 4195221, 4541725

Offset: 1

Seiichi Manyama, May 04 2021

q[n_] := n == 1 || Mod[Sum[PowerMod[-k, k, n], {k, 1, n}], n] == 1; Select[Range[5000], q] (* Amiram Eldar, May 04 2021 *)

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

a(11)-a(13) from Chai Wah Wu, May 04 2021
a(14) from Martin Ehrenstein, May 05 2021
a(15)-a(17) from Martin Ehrenstein, May 08 2021

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

A343930 Numbers k such that Sum_{j=1..k} (-j)^j == 1 (mod k).

Views

Author

Keywords

Crossrefs

Programs

Mathematica

PARI

Extensions