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A134126
Indices k such that the (k+1)-st partial sum of primes divided by k is integer.
5
1, 2, 4, 7, 10, 50, 130, 328, 651, 4938, 7492, 8083, 12045, 33170, 43138, 61690, 151496, 265056, 953959, 1971358, 5084552, 9372007, 25274899, 34120615, 38684178, 44161681, 415148959, 1294318767, 3955750033, 6484256906, 21755550341, 22058148324
OFFSET
1,2
COMMENTS
The corresponding quotients are given in A134125.
FORMULA
Such integers k>0 that A007504(k+1) == 0 (mod k).
EXAMPLE
The indices k = 3, 5, 6, 8, etc. do not produce integer quotients and do not appear in the sequence.
PROG
(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
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Enoch Haga, Oct 09 2007
EXTENSIONS
Edited by R. J. Mathar, Apr 17 2009
More terms from Sean A. Irvine, Dec 08 2010
a(27), a(28) from D. S. McNeil, Dec 08 2010
a(29) from Max Alekseyev, Jan 28 2012
a(30)-a(32) from Amiram Eldar, Apr 30 2024
STATUS
approved