

A233577


Prime(n), where n is such that (1+sum_{i=1..n} prime(i)^18) / n is an integer.


1



2, 3, 5, 7, 13, 17, 19, 23, 37, 43, 61, 67, 73, 89, 103, 107, 151, 163, 179, 181, 197, 223, 251, 263, 269, 307, 347, 359, 373, 383, 433, 491, 587, 593, 613, 619, 701, 751, 761, 881, 997, 1019, 1129, 1321, 1439, 1601, 1699, 1951, 2069, 2243, 2267, 2297, 2423
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OFFSET

1,1


COMMENTS

a(516) > 1066173339601.


LINKS

Robert Price, Table of n, a(n) for n = 1..515
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^18+1 = 118016956494132483318 when divided by 6 equals 19669492749022080553 which is an integer.


MATHEMATICA

t = {}; sm = 1; Do[sm = sm + Prime[n]^18; 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)^18); 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: A052015 A042992 A255203 * A233041 A049567 A293048
Adjacent sequences: A233574 A233575 A233576 * A233578 A233579 A233580


KEYWORD

nonn


AUTHOR

Robert Price, Dec 13 2013


STATUS

approved



