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A007506
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Primes p with property that p divides the sum of all primes <= p.
(Formerly M1554)
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12
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OFFSET
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1,1
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COMMENTS
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a(6), if it exists, is larger than 10^14. - Giovanni Resta, Jan 09 2014
Also primes p with property that p divides 1 plus the sum of all composites < p. - Vicente Izquierdo Gomez, Aug 05 2014
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REFERENCES
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J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 71, p. 25, Ellipses, Paris 2008.
Harry L. Nelson, Prime Sums, J. Rec. Math., 14 (1981), 205-206.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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EXAMPLE
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2 divides 2;
5 divides 2 + 3 + 5;
71 divides 2 + 3 + 5 + 7 + ... + 61 + 67 + 71; etc.
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MATHEMATICA
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sumOfPrimes = 0; Do[ sumOfPrimes += p; If[ Divisible[ sumOfPrimes, p], Print[p]], {p, Prime /@ Range[23000000]}] (* Jean-François Alcover, Oct 22 2012 *)
Transpose[Module[{nn=23000000, pr}, pr=Prime[Range[nn]]; Select[Thread[ {Accumulate[ pr], pr}], Divisible[#[[1]], #[[2]]]&]]][[2]] (* Harvey P. Dale, Feb 09 2013 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,nice,hard,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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