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A233575 Prime(n), where n is such that (sum_{i=1..n} prime(i)^18) / n is an integer. 0
2, 157, 1697, 190573, 167719729, 22092660553, 57613776809 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(8) > 1066173339601.

LINKS

Table of n, a(n) for n=1..7.

OEIS Wiki, Sums of powers of primes divisibility sequences

FORMULA

a(n) = prime(A131278(n)).

EXAMPLE

a(2) = 157, because 157 is the 37th prime and the sum of the first 37 primes^18 = 7222759943091280921446062146835136523956 when divided by 37 equals 195209728191656241120163841806355041188 which is an integer.

MATHEMATICA

t = {}; sm = 0; 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

(PARI) S=n=0; forprime(p=1, , (S+=p^18)%n++||print1(p", ")) \\ - M. F. Hasler, Dec 01 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: A284458 A260886 A142006 * A233263 A124225 A159030

Adjacent sequences:  A233572 A233573 A233574 * A233576 A233577 A233578

KEYWORD

nonn,more

AUTHOR

Robert Price, Dec 13 2013

STATUS

approved

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Last modified January 28 00:32 EST 2020. Contains 331313 sequences. (Running on oeis4.)