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%I #25 May 05 2021 18:08:43
%S 1,2,4,6,10,12,52,74,136,242,305,670,1431,1706,1713,3956,18331,22238,
%T 25162,107332,162778,169479,431228,459704,1808681,1813273,5954563,
%U 10351930,27931668,32490143,201039164,311357190,733854046,1677164490,3722808264,9000784596
%N Numbers k such that k divides 1 + Sum_{j=1..k} prime(j)^13.
%C a(47) > 1.4*10^13. - _Bruce Garner_, May 05 2021
%H Bruce Garner, <a href="/A233349/b233349.txt">Table of n, a(n) for n = 1..46</a>
%H OEIS Wiki, <a href="https://oeis.org/wiki/Sums_of_primes_divisibility_sequences">Sums of powers of primes divisibility sequences</a>
%e a(5) = 10 because 1 plus the sum of the first 10 primes^13 is 10816960132320284800 which is divisible by 10.
%t p = 2; k = 0; s = 1; lst = {}; While[k < 40000000000, s = s + p^13; 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 07 2013