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A134129 Prime partial sums A007504(k+1) such that A007504(k+1)/k is an integer.

%I A134129 #15 Jan 09 2025 02:13:34
%S A134129 5,10,28,77,160,5350,43940,331608,1464099,111509916,269629588,
%T A134129 316586861,734973855,6186337680,10731699088,22692172980,148089006456,
%U A134129 474639489984,6777589645423,30458742769120,215730372141680,761593852850347,5875984874989879,10893969051902225
%N A134129 Prime partial sums A007504(k+1) such that A007504(k+1)/k is an integer.
%C A134129 See A134125 and cross-references.
%H A134129 Amiram Eldar, <a href="/A134129/b134129.txt">Table of n, a(n) for n = 1..32</a>
%F A134129 a(n) = A007504(A134126(n+1)) .
%e A134129 A007504(2)/1 = 5/1 = 5 is an integer, so 5 is added to the sequence.
%e A134129 A007504(3)/2 = 10/2 = 5 is an integer, so 10 is added to the sequence.
%e A134129 A007504(4)/3 = 17/3 is not an integer, so 17 is not added to the sequence.
%o A134129 (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 A134129 (PARI) lista(pmax) = {my(k = 0, s = 2); forprime(p = 3, pmax, k++; s += p; if(!(s % k), print1(s, ", ")));} \\ _Amiram Eldar_, Apr 30 2024
%Y A134129 Cf. A007504, A134125, A134126 A134127, A134128.
%K A134129 nonn
%O A134129 1,1
%A A134129 _Enoch Haga_, Oct 09 2007
%E A134129 Edited by _R. J. Mathar_, May 15 2009
%E A134129 a(21)-a(24) from _Amiram Eldar_, Apr 30 2024