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%I #25 Jun 06 2021 15:50:25
%S 1,2,3,4,5,6,8,9,10,12,15,16,17,20,24,27,30,32,34,39,40,45,48,51,55,
%T 57,60,64,68,80,85,90,96,100,102,120,128,136,160,168,170,180,186,192,
%U 204,205,216,230,238,240,255,272,285,320,340,360,384,408,480,510
%N Numbers k such that k divides 1 + Sum_{j=1..k} prime(j)^16.
%C a(616) > 1.5*10^13. - _Bruce Garner_, Jun 06 2021
%H Bruce Garner, <a href="/A233461/b233461.txt">Table of n, a(n) for n = 1..615</a> (first 479 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(9)=10 because 1 plus the sum of the first 10 primes^16 is 256716898101196243797130 which is divisible by 10.
%t p = 2; k = 0; s = 1; lst = {}; While[k < 40000000000, s = s + p^16; 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 10 2013