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%I #32 Jun 06 2021 15:50:46
%S 1,2,3,4,6,7,8,9,12,14,18,19,21,24,27,28,36,38,41,42,45,48,54,56,57,
%T 63,69,72,74,76,84,94,107,108,112,114,126,133,135,152,168,171,189,216,
%U 228,252,266,297,312,334,336,342,360,378,380,399,423,432,441,444
%N Numbers k such that k divides 1 + Sum_{j=1..k} prime(j)^18.
%C a(681) > 1.5*10^13. - _Bruce Garner_, Jun 06 2021
%H Bruce Garner, <a href="/A233576/b233576.txt">Table of n, a(n) for n = 1..680</a> (first 515 terms from Robert Price, terms 516..559 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 6 is a term because 1 plus the sum of the first 6 primes^18 is 118016956494132483318 which is divisible by 6.
%t p = 2; k = 0; s = 1; lst = {}; While[k < 40000000000, s = s + p^18; 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 13 2013
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