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A233767 Prime(n), where n is such that (sum_{i=1..n} prime(i)^19) / n is an integer. 0
2, 97, 3203, 5059, 6469, 8081, 35051, 39719, 42209, 109049, 154591, 523297, 6621827, 20059771, 258196441, 731584957, 1427109029, 1899496631, 8428550519, 50790885203 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(21) > 1066173339601.

LINKS

Table of n, a(n) for n=1..20.

OEIS Wiki, Sums of powers of primes divisibility sequences

FORMULA

a(n) = prime(A131279(n)).

EXAMPLE

a(2) = 97, because 97 is the 25th prime and the sum of the first 25 primes^19 = 71486619210134792705255313675343157050 when divided by 25 equals 2859464768405391708210212547013726282 which is an integer.

MATHEMATICA

t = {}; sm = 0; 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

(PARI) S=n=0; forprime(p=1, , (S+=p^19)%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: A042151 A233192 A065592 * A223936 A224083 A285023

Adjacent sequences:  A233764 A233765 A233766 * A233768 A233769 A233770

KEYWORD

nonn,more,less

AUTHOR

Robert Price, Dec 15 2013

STATUS

approved

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Last modified May 24 21:25 EDT 2017. Contains 287008 sequences.