A343983 Numbers k such that Sum_{j|k} j^j == 1 (mod k).

1, 2, 3, 4, 5, 7, 9, 11, 13, 17, 19, 23, 25, 27, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 72, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 127, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257

Offset: 1

Author

Seiichi Manyama, May 06 2021

Keywords

• nonn

Comments

This sequence is different from A074583.

Links

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

Crossrefs

Cf. A062796, A188776.

Programs

Mathematica

q[n_] := Divisible[DivisorSum[n, #^# &] - 1, n]; Select[Range[260], q] (* Amiram Eldar, May 06 2021 *)

PARI

isok(n) = sumdiv(n, d, Mod(d, n)^d)==1;

Python

from itertools import count, islice
from sympy import divisors
def A343983_gen(): # generator of terms
    yield 1
    for k in count(1):
        if sum(pow(j,j,k) for j in divisors(k,generator=True)) % k == 1:
            yield k
A343983_list = list(islice(A343983_gen(),30)) # Chai Wah Wu, Jun 19 2022