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

%I A343983 #17 Jun 19 2022 15:23:26
%S A343983 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,
%T A343983 71,72,73,79,83,89,97,101,103,107,109,113,121,125,127,131,137,139,149,
%U A343983 151,157,163,167,169,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257
%N A343983 Numbers k such that Sum_{j|k} j^j == 1 (mod k).
%C A343983 This sequence is different from A074583.
%H A343983 Seiichi Manyama, <a href="/A343983/b343983.txt">Table of n, a(n) for n = 1..10000</a>
%t A343983 q[n_] := Divisible[DivisorSum[n, #^# &] - 1, n]; Select[Range[260], q] (* _Amiram Eldar_, May 06 2021 *)
%o A343983 (PARI) isok(n) = sumdiv(n, d, Mod(d, n)^d)==1;
%o A343983 (Python)
%o A343983 from itertools import count, islice
%o A343983 from sympy import divisors
%o A343983 def A343983_gen(): # generator of terms
%o A343983     yield 1
%o A343983     for k in count(1):
%o A343983         if sum(pow(j,j,k) for j in divisors(k,generator=True)) % k == 1:
%o A343983             yield k
%o A343983 A343983_list = list(islice(A343983_gen(),30)) # _Chai Wah Wu_, Jun 19 2022
%Y A343983 Cf. A062796, A188776.
%K A343983 nonn
%O A343983 1,2
%A A343983 _Seiichi Manyama_, May 06 2021