A233767 Prime(n), where n is such that (Sum_{i=1..n} prime(i)^19) / n is an integer.

2, 97, 3203, 5059, 6469, 8081, 35051, 39719, 42209, 109049, 154591, 523297, 6621827, 20059771, 258196441, 731584957, 1427109029, 1899496631, 8428550519, 50790885203, 7475902096387, 22626378502139, 38855796912367, 162082298018497, 589085299527401, 4271778258271487

Offset

1,1

Comments

a(26) > 661876608760109. - Bruce Garner, Jun 30 2021

a(27) > 4699724194264849. - Paul W. Dyson, Jun 27 2023

Links

Table of n, a(n) for n=1..26.

OEIS Wiki, Sums of powers of primes divisibility sequences

Formula

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

Example

97 is a term, 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) my(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,less

Author

Robert Price, Dec 15 2013

Extensions

a(21) from Karl-Heinz Hofmann, Feb 24 2021

a(22) from Bruce Garner, Mar 01 2021

a(23) from Bruce Garner, Mar 08 2021

a(24) from Bruce Garner, Apr 14 2021

a(25) from Bruce Garner, Jun 30 2021

a(26) from Paul W. Dyson, Jun 27 2023

Status

approved