A233555 - OEIS

%I #46 Sep 15 2023 21:30:36

%S 2,5724469,10534369,16784723,33330911,189781037,8418091991,

%T 58605633953,109388266843,448366797199,1056238372873,24603683667221,

%U 86982253895059,100316149840769,164029709175817,542295448805641,685217940914237,1701962315686097,23064173255594491

%N Prime(m), where m is such that (Sum_{i=1..m} prime(i)^17) / m is an integer.

%C a(18) > 1005368767096627. - _Bruce Garner_, Aug 30 2021

%C a(19) > 1701962315686097. - _Bruce Garner_, Jan 07 2022

%H OEIS Wiki, <a href="https://oeis.org/wiki/Sums_of_primes_divisibility_sequences">Sums of powers of primes divisibility sequences</a>

%F a(n) = prime(A131277(n)).

%e a(1) = 2, because 2 is the 1st prime and the sum of the first 1 primes^17 = 131072 when divided by 1 equals 131072 which is an integer.

%t t = {}; sm = 0; Do[sm = sm + Prime[n]^17; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)

%o (PARI) is(n)=if(!isprime(n),return(0)); my(t=primepi(n),s); forprime(p=2,n,s+=Mod(p,t)^17); s==0 \\ _Charles R Greathouse IV_, Nov 30 2013

%o (PARI) S=n=0;forprime(p=1,,(S+=p^17)%n++||print1(p",")) \\ _M. F. Hasler_, Dec 01 2013

%Y Cf. A085450 (smallest m > 1 that divide Sum_{k=1..m} prime(k)^n).

%Y Cf. A000040, A007504, A045345, A171399, A128165, A233523, A050247, A050248.

%Y Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.

%K nonn

%O 1,1

%A _Robert Price_, Dec 12 2013

%E a(12) from _Bruce Garner_, Mar 02 2021

%E a(13) from _Bruce Garner_, Mar 17 2021

%E a(14) from _Bruce Garner_, Mar 30 2021

%E a(15) from _Bruce Garner_, Apr 14 2021

%E a(16) from _Bruce Garner_, Jun 30 2021

%E a(17) from _Bruce Garner_, Aug 30 2021

%E a(18) from _Bruce Garner_, Jan 07 2022

%E a(19) from _Paul W. Dyson_, Sep 15 2023