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%I #38 Jun 02 2021 04:37:42
%S 1,2,4,6,10,12,116,147,324,2070,2902,3663,4994,11531,13554,22421,
%T 558905,1242890,1655487,2021278,2878297,4790338,7061177,16875261,
%U 21813642,24563860,58919808,69676102,85356321,92610708,205600836,338430087,343675600,1176903461,1698127637,4657254361,17421656611
%N Numbers k such that k divides 1 + Sum_{j=1..k} prime(j)^17.
%C a(45) > 1.5*10^13. - _Bruce Garner_, Jun 02 2021
%H Bruce Garner, <a href="/A233556/b233556.txt">Table of n, a(n) for n = 1..44</a> (first 37 terms from Robert Price, terms 38..39 from Karl-Heinz Hofmann)
%H OEIS Wiki, <a href="https://oeis.org/wiki/Sums_of_primes_divisibility_sequences">Sums of powers of primes divisibility sequences</a>
%e 10 is a term because 1 plus the sum of the first 10 primes^17 is 7404514559506748686057600 which is divisible by 10.
%t p = 2; k = 0; s = 1; lst = {}; While[k < 40000000000, s = s + p^17; 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 12 2013