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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

Table of n, a(n) for n=1..42.

OEIS Wiki, Sums of powers of primes divisibility sequences

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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Last modified May 28 02:58 EDT 2017. Contains 287211 sequences.