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

1,2

Comments

This sequence is different from A074583.

Links

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A062796, A188776.

Sequence in context: A081998 A325266 A284288 * A074583 A001092 A327782

Adjacent sequences: A343980 A343981 A343982 * A343984 A343985 A343986

Keyword

nonn

Author

Seiichi Manyama, May 06 2021

Status

approved