A233575 Prime(m), where m is such that (Sum_{i=1..m} prime(i)^18) / m is an integer.

2, 157, 1697, 190573, 167719729, 22092660553, 57613776809, 4386989244577, 91982826261331, 13432259712845291

Offset: 1

Author

Robert Price, Dec 13 2013

Keywords

• nonn
• more

Comments

a(9) > 36730498487251. - Paul W. Dyson, Jan 08 2021

a(10) > 93400375993241. - Bruce Garner, Mar 17 2021

a(11) > 18205684894350047. - Paul W. Dyson, Dec 16 2024

Examples

			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.
		

Links

• 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 = 0; 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

PARI

S=n=0;forprime(p=1,,(S+=p^18)%n++||print1(p",")) \\ - M. F. Hasler, Dec 01 2013

Formula

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

Extensions

a(8) from Paul W. Dyson, Jan 08 2021

a(9) from Bruce Garner, Mar 17 2021

a(10) from Paul W. Dyson, Oct 03 2023