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%I #24 Jun 02 2021 04:21:13
%S 1,2,3,4,6,8,9,12,13,24,26,28,45,48,88,168,360,474,540,550,864,1104,
%T 1230,1408,1488,1816,2367,2677,3507,5592,5916,6612,11238,12925,14124,
%U 23523,24087,27356,41528,43465,56951,74688,79244,86682,181730,186136,193704
%N Numbers k such that k divides 1 + Sum_{j=1..k} prime(j)^14.
%C a(120) > 2*10^13. - _Bruce Garner_, Jun 02 2021
%H Bruce Garner, <a href="/A232966/b232966.txt">Table of n, a(n) for n = 1..119</a> (first 101 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(7)=9 because 1 plus the sum of the first 9 primes^14 is 12564538647431705217 which is divisible by 9.
%t p = 2; k = 0; s = 1; lst = {}; While[k < 40000000000, s = s + p^14; If[Mod[s, ++k] == 0, AppendTo[lst, k]; Print[{k, p}]]; p = NextPrime@ p] (* derived from A128169 *)
%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 1,2
%A _Robert Price_, Dec 02 2013
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