|
|
A007506
|
|
Primes p with property that p divides the sum of all primes <= p.
(Formerly M1554)
|
|
12
|
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
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
|
|
REFERENCES
|
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).
|
|
LINKS
|
|
|
EXAMPLE
|
2 divides 2;
5 divides 2 + 3 + 5;
71 divides 2 + 3 + 5 + 7 + ... + 61 + 67 + 71; etc.
|
|
MAPLE
|
for n from 1 to q do a:=a+ithprime(n); if gcd(ithprime(n), a)>1 then print(ithprime(n)); fi; od; end:
|
|
MATHEMATICA
|
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 *)
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,nice,hard,more
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|