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 A233769 Prime(n), where n is such that (1+sum_{i=1..n} prime(i)^19) / n is an integer. 0
 2, 3, 7, 11, 13, 29, 37, 241, 1429, 2437, 2741, 4583, 7333, 8269, 36073, 37397, 48121, 73037, 130261, 147289, 280037, 1032259, 6594787, 10249573, 130193849, 443038781, 527454197, 1024907927, 1736090963, 2602512709, 13517865841, 13684220029, 64209198247, 93380481511, 126718347859, 143176188581, 231059158871, 273286859737, 511940464493, 512760363097, 715173864563, 810985955573 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(43) > 1066173339601. LINKS EXAMPLE a(5) = 13, because 13 is the 6th prime and the sum of the first 6 primes^19+1 = 1523090798793695143992 when divided by 6 equals 253848466465615857332 which is an integer. MATHEMATICA t = {}; sm = 1; Do[sm = sm + Prime[n]^19; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *) PROG (PARI) is(n)=if(!isprime(n), return(0)); my(t=primepi(n), s); forprime(p=2, n, s+=Mod(p, t)^19); s==0 \\ Charles R Greathouse IV, Nov 30 2013 CROSSREFS Cf. A085450 = smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n. Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248. Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601. Sequence in context: A233863 A233194 A233040 * A038895 A113244 A040152 Adjacent sequences:  A233766 A233767 A233768 * A233770 A233771 A233772 KEYWORD nonn AUTHOR Robert Price, Dec 15 2013 STATUS approved

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