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A045345
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Numbers n such that n divides sum of first n primes A007504(n).
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36
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1, 23, 53, 853, 11869, 117267, 339615, 3600489, 96643287, 2664167025, 43435512311, 501169672991
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(10) and a(11) were found by Giovanni Resta (Nov 15 2004). He states that there are no other terms for primes p < 4011201392413. See link to Prime Puzzles, Puzzle 31 below. - Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 21 2006
a(13) > pi(2*10^13). [From Donovan Johnson (donovan.johnson(AT)yahoo.com), Aug 23 2010]
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LINKS
| Eric Weisstein's World of Mathematics, Prime Sums
The Prime Puzzles & Problems Connection: Puzzle 31.- The Average Prime number, APN(k) = S(Pk)/k.
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MATHEMATICA
| s = 0; t = {}; Do[s = s + Prime[n]; If[ Mod[s, n] == 0, AppendTo[t, n]], {n, 1000000}]; t - Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 21 2006
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PROG
| via Wolfram Alpha, input: (sum(prime(n), n=1..23)) mod 23 for example [Bill McEachen, Feb 23 2011]
(PARI) s=0; n=0; forprime(p=2, 1e7, s+=p; if(s%n++==0, print1(n", "))) \\ Charles R Greathouse IV, Jul 15 2011
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CROSSREFS
| Cf. A007504, A024450, A111441, A098999, A122140, A122102, A122141, A122103, A122142.
Sequence in context: A171432 A078854 A078959 * A133986 A103006 A053236
Adjacent sequences: A045342 A045343 A045344 * A045346 A045347 A045348
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KEYWORD
| nonn,nice
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AUTHOR
| Jud McCranie (JudMcCranie(AT)ugaalum.uga.edu)
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EXTENSIONS
| More terms from Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 21 2006
a(12) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Aug 23 2010
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