A233577 Prime(k), where k is such that (1+Sum_{i=1..k} prime(i)^18) / k is an integer.

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

Offset: 1

Author

Robert Price, Dec 13 2013

Keywords

• nonn

Comments

a(681) > 491952295618219. - Bruce Garner, Jun 06 2021

Examples

			13 is a term 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.
		

Links

• Bruce Garner, Table of n, a(n) for n = 1..680 (first 515 terms from Robert Price, terms 516..559 from Karl-Heinz Hofmann)
• OEIS Wiki, Sums of powers of primes divisibility sequences

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.

Programs

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 *)

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