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%I #55 Jun 06 2021 06:42:12
%S 1,2,3,4,5,6,7,8,9,10,12,13,14,15,16,18,20,21,24,26,27,28,30,35,36,39,
%T 40,42,45,46,48,52,54,56,60,63,65,66,70,72,78,80,84,87,90,91,100,104,
%U 105,112,117,120,126,130,138,140,144,154,156,160,168,175,176
%N Numbers k such that k divides 1 + Sum_{j=1..k} prime(j)^12.
%C a(1171) > 2*10^13. - _Bruce Garner_, Jun 06 2021
%H Bruce Garner, <a href="/A233264/b233264.txt">Table of n, a(n) for n = 1..1170</a> (terms 1..907 from Robert Price, terms 908..967 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 5 is a term because 1 plus the sum of the first 11 primes^12 is 3152514340085 which is divisible by 11.
%p A233264:=n->if type((1+add(ithprime(i)^12, i=1..n))/n, integer) then n; fi; seq(A233264(n), n=1..200); # _Wesley Ivan Hurt_, Dec 06 2013
%t p = 2; k = 0; s = 1; lst = {}; While[k < 41000000000, s = s + p^12; If[Mod[s, ++k] == 0, AppendTo[lst, k]; Print[{k, p}]]; p = NextPrime@ p] (* derived from A128169 *)
%t With[{nn=200},Transpose[Select[Thread[{Accumulate[Prime[Range[nn]]^12], Range[nn]}], Divisible[#[[1]]+1,#[[2]]]&]][[2]]] (* _Harvey P. Dale_, May 28 2015 *)
%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 06 2013
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