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%I #21 Aug 24 2021 10:14:37
%S 1,3,57,32547,9961491,297381939,1338104811,3942759027,5688011361,
%T 8920514307,9146532873,40253706489,243640690617,764039295291,
%U 1127102902923,1556475424971,2251315404417,3005607686883,5222670270483
%N Numbers k such that k^3 divides 2^(k^2)+1.
%C If k belongs to this sequence, then so does (2^(k^2)+1)/k^2.
%C From _Alexander Adamchuk_, May 14 2010: (Start)
%C 3 divides a(n) for n>1.
%C 19 divides a(n) for n>2. (End)
%H ArtOfProblemSolving forum, <a href="http://www.artofproblemsolving.com/Forum/viewtopic.php?p=796197">n^3 | (2^{n^2}+1)</a>
%t Select[Range[100000], Divisible[2^(#^2) + 1, #^3] &] (* _Robert Price_, Mar 23 2020 *)
%Y Cf. A006521, A093546, A093665, A136372, A128677.
%Y Cf. A128678, A128679, A128680, A128681, A128682, A128683, A128684, A128685, A177813, A177814, A177816, A177817, A177818, A177819, A177820.
%K nonn
%O 1,2
%A _Max Alekseyev_, Mar 27 2007, Mar 29 2007, Apr 18 2007
%E a(7) from _Ryan Propper_, Jan 01 2008
%E a(8)-a(19) from _Max Alekseyev_, May 14 2010
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