A233040 - OEIS

%I #27 Apr 07 2021 20:08:53

%S 2,3,7,11,13,29,37,199,15679,18211,59359,78203,84533,166399,528299,

%T 639697,2080651,2914033,5687413,73463179,112760273,156196991,

%U 278840981,503948113,3706314893,3786209711,12626179519,13551633533,13844655553,24074338279,37937104823

%N Prime(n), where n is such that (1 + Sum_{i=1..n} prime(i)^7) / n is an integer.

%C a(43) > 458158058915101. - _Bruce Garner_, Apr 07 2021

%H Bruce Garner, <a href="/A233040/b233040.txt">Table of n, a(n) for n = 1..42</a> (first 35 terms from Robert Price)

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

%e a(4) = 11, because 11 is the 5th prime and the sum of the first 5 primes^7+1 = 20391155 when divided by 5 equals 4078231, which is an integer.

%t t = {}; sm = 1; Do[sm = sm + Prime[n]^7; 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)^7); s==0 \\ _Charles R Greathouse IV_, Nov 30 2013

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

%Y Cf. 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 03 2013