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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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48
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1, 23, 53, 853, 11869, 117267, 339615, 3600489, 96643287, 2664167025, 43435512311, 501169672991, 745288471601
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OFFSET
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1,2
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COMMENTS
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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, Aug 21 2006
a(13) > pi(2*10^13). - Donovan Johnson, Aug 23 2010
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LINKS
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Table of n, a(n) for n=1..13.
Javier Cilleruelo and Florian Luca, On the sum of the first n primes, Q. J. Math. 59:4 (2008), 14 pp.
Kaisa Matomäki, A note on the sum of the first n primes, Quart. J. Math. 61 (2010), pp. 109-115.
The Prime Puzzles & Problems Connection: Puzzle 31.- The Average Prime number, APN(k) = S(Pk)/k.
Eric Weisstein's World of Mathematics, Prime Sums
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FORMULA
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Matomäki proves that a(n) >> n^(24/19). - Charles R Greathouse IV, Jun 13 2012
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MATHEMATICA
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s = 0; t = {}; Do[s = s + Prime[n]; If[ Mod[s, n] == 0, AppendTo[t, n]], {n, 1000000}]; t - Alexander Adamchuk, Aug 21 2006
nn=4000000; With[{acpr=Accumulate[Prime[Range[nn]]]}, Select[Range[nn], Divisible[ acpr[[#]], #]&]] (* Harvey P. Dale, Sep 14 2012 *)
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PROG
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(Wolfram Alpha) (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
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Cf. A007504, A171399, A024450, A111441, A098999, A122140, A122102, A122141, A122103, A122142, A050247, A050248.
Sequence in context: A171432 A078854 A078959 * A133986 A103006 A053236
Adjacent sequences: A045342 A045343 A045344 * A045346 A045347 A045348
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KEYWORD
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nonn,nice,more,changed
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AUTHOR
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Jud McCranie
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EXTENSIONS
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More terms from Alexander Adamchuk, Aug 21 2006
a(12) from Donovan Johnson, Aug 23 2010
a(13) from Robert Price, Mar 17 2013
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STATUS
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approved
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