cp's OEIS Frontend

A134126 Indices k such that the (k+1)-st partial sum of primes divided by k is an integer.

%I A134126 #24 Jan 09 2025 02:14:28
%S A134126 1,2,4,7,10,50,130,328,651,4938,7492,8083,12045,33170,43138,61690,
%T A134126 151496,265056,953959,1971358,5084552,9372007,25274899,34120615,
%U A134126 38684178,44161681,415148959,1294318767,3955750033,6484256906,21755550341,22058148324
%N A134126 Indices k such that the (k+1)-st partial sum of primes divided by k is an integer.
%C A134126 The corresponding quotients are given in A134125.
%F A134126 Such integers k>0 that A007504(k+1) == 0 (mod k).
%e A134126 The indices k = 3, 5, 6, 8, etc. do not produce integer quotients and do not appear in the sequence.
%o A134126 (UBASIC) 10 'primes using counters 20 N=3:C=1:R=5:print 2;3,5 30 A=3:S=sqrt(N) 40 B=N\A 50 if B*A=N then N=N+2:goto 30 60 A=A+2:O=A 70 if A<=sqrt(N) then 40 80 C=C+1 90 R=R+N:T=R/C:U=R-N 100 if T=int(T) then print C;U;N;R;T:stop 110 N=N+2:goto 30
%o A134126 (PARI) lista(pmax) = {my(k = 0, s = 2); forprime(p = 3, pmax, k++; s += p; if(!(s % k), print1(k, ", ")));} \\ _Amiram Eldar_, Apr 30 2024
%Y A134126 Cf. A007504, A134125, A134127, A134128, A134129.
%K A134126 nonn,more
%O A134126 1,2
%A A134126 _Enoch Haga_, Oct 09 2007
%E A134126 Edited by _R. J. Mathar_, Apr 17 2009
%E A134126 More terms from _Sean A. Irvine_, Dec 08 2010
%E A134126 a(27), a(28) from _D. S. McNeil_, Dec 08 2010
%E A134126 a(29) from _Max Alekseyev_, Jan 28 2012
%E A134126 a(30)-a(32) from _Amiram Eldar_, Apr 30 2024