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%I #17 May 11 2023 09:20:18
%S 1,2,4,7,10,50,130,328,651,4938,7492,8083,12045,33170,43138,61690,
%T 151496,265056,953959,1971358,5084552,9372007,25274899,34120615,
%U 38684178,44161681,415148959,1294318767,3955750033
%N Indices k such that the (k+1)st partial sum of primes divided by k is integer.
%C The corresponding quotients are given in A134125.
%F Such integers k>0 that A007504(k+1) == 0 (mod k).
%e The indices k=3, 5, 6, 8 etc. do not produce integer quotients and do not appear in the sequence.
%o (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
%Y Cf. A134125, A134127, A134128, A134129.
%K nonn
%O 1,2
%A _Enoch Haga_, Oct 09 2007
%E Edited by _R. J. Mathar_, Apr 17 2009
%E More terms from _Sean A. Irvine_, Dec 08 2010
%E a(27), a(28) from _D. S. McNeil_, Dec 08 2010
%E a(29) from _Max Alekseyev_, Jan 28 2012
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