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A128981 Numbers k such that k divides Sum_{j=1..k} j^j = A001923(k).

%I A128981 #55 Dec 31 2023 11:29:48
%S A128981 1,4,17,19,148,1577,3564,4388,5873,6639,8579,62500,376636,792949,
%T A128981 996044,1174065,3333551,5179004,7516003
%N A128981 Numbers k such that k divides Sum_{j=1..k} j^j = A001923(k).
%C A128981 a(20) > 10^7. - _Hiroaki Yamanouchi_, Aug 25 2015
%p A128981 a:=0:
%p A128981 for n from 1 to 2000 do
%p A128981     a:=a+n^n:
%p A128981     if a mod n=0 then
%p A128981         print(n);
%p A128981     fi;
%p A128981 od: # Revised program from _R. J. Mathar_, Jun 18 2015
%t A128981 f=0; Do[ f=f+k^k; If[ IntegerQ[f/k], Print[k] ], {k,1,6639} ]
%o A128981 (PARI) for(n=1,10^4, s=sum(i=1,n,Mod(i,n)^i); if(!Mod(s,n), print1(n,", "))) \\ _Derek Orr_, Jun 18 2015
%o A128981 (Python)
%o A128981 from itertools import accumulate, count, islice
%o A128981 def A128981_gen(): # generator of terms
%o A128981     yield 1
%o A128981     for i, j in enumerate(accumulate(k**k for k in count(1)),start=2):
%o A128981         if j % i == 0:
%o A128981             yield i
%o A128981 A128981_list = list(islice(A128981_gen(),10)) # _Chai Wah Wu_, Jun 18 2022
%Y A128981 Cf. A062970, A001923.
%K A128981 hard,more,nonn
%O A128981 1,2
%A A128981 _Alexander Adamchuk_, Apr 29 2007
%E A128981 a(11) and a(12) from _Jon E. Schoenfield_, May 09 2007
%E A128981 a(13) = 376636 from _Alexander Adamchuk_, May 03 2010
%E A128981 a(14)-a(16) from _Lars Blomberg_, May 10 2011
%E A128981 a(17) from _Giovanni Resta_, Jul 13 2015
%E A128981 a(18)-a(19) from _Hiroaki Yamanouchi_, Aug 25 2015