A188776 - OEIS

%I #39 Jun 20 2022 04:18:13

%S 1,2,9,30,6871,185779,208541,813162,864355,2573155

%N Numbers n such that Sum_{k=1..n} k^k == 1 (mod n).

%C Numbers n such that A001923(n) == 1 (mod n).

%C a(11) > 10^7. - _Hiroaki Yamanouchi_, Aug 25 2015

%t Union@Table[If[Mod[Sum[PowerMod[i,i,n],{i,1,n}],n]==1,Print[n];n],{n,1,20000}]

%o (PARI)

%o f(n)=lift(sum(k=1, n, Mod(k, n)^k));

%o for(n=1, 10^6, if(f(n)==1, print1(n, ", "))) /* _Joerg Arndt_, Apr 10 2011 */

%o (Python)

%o from itertools import accumulate, count, islice

%o def A188776_gen(): # generator of terms

%o     yield 1

%o     for i, j in enumerate(accumulate(k**k for k in count(2)),start=2):

%o         if not j % i:

%o             yield i

%o A188776_list = list(islice(A188776_gen(),5)) # _Chai Wah Wu_, Jun 18 2022

%Y Cf. A001923, A128981 (sum == 0 mod n), A188775 (sum == -1 mod n).

%K nonn,more

%O 1,2

%A _José María Grau Ribas_, Apr 10 2011

%E a(6)-a(9) from _Lars Blomberg_, May 10 2011

%E a(1) inserted and a(10) added by _Hiroaki Yamanouchi_, Aug 25 2015