cp's OEIS Frontend

A233414 Prime(n), where n is such that (1 + Sum_{i=1..n} prime(i)^15) / n is an integer.

%I A233414 #33 Jun 02 2021 05:47:07
%S A233414 2,3,7,11,13,29,37,43,79,373,2719,3767,4583,6653,34919,83737,95383,
%T A233414 493523,741053,1433689,1629623,2254757,2686819,2801221,7283587,
%U A233414 12288799,49986019,120365039,1280220301,1388048693,2336739481,3390500677,5139223693,14729858701
%N A233414 Prime(n), where n is such that (1 + Sum_{i=1..n} prime(i)^15) / n is an integer.
%C A233414 a(49) > 661876608760109. - _Bruce Garner_, Jun 02 2021
%H A233414 Bruce Garner, <a href="/A233414/b233414.txt">Table of n, a(n) for n = 1..48</a> (first 43 terms from Robert Price)
%H A233414 OEIS Wiki, <a href="https://oeis.org/wiki/Sums_of_primes_divisibility_sequences">Sums of powers of primes divisibility sequences</a>
%e A233414 a(3) = 7, because 7 is the 4th prime and the sum of the first 4 primes^15+1 = 4778093469744 when divided by 4 equals 1194523367436 which is an integer.
%t A233414 t = {}; sm = 1; Do[sm = sm + Prime[n]^15; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
%t A233414 nn=7000000;With[{pr15=Accumulate[Prime[Range[nn]]^15]+1}, Prime[ #]&/@ Select[ Range[nn],Divisible[pr15[[#]],#]&]] (* This program will generate the first 28 terms of the sequence.  To generate an additional 6 terms terms, nn would have to equal 659 million, and the program would take a long time to run. *) (* _Harvey P. Dale_, May 01 2014 *)
%o A233414 (PARI) is(n)=if(!isprime(n),return(0)); my(t=primepi(n),s); forprime(p=2,n,s+=Mod(p,t)^15); s==0 \\ _Charles R Greathouse IV_, Nov 30 2013
%Y A233414 Cf. A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).
%Y A233414 Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.
%Y A233414 Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.
%K A233414 nonn
%O A233414 1,1
%A A233414 _Robert Price_, Dec 09 2013