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%I #17 Sep 17 2018 03:15:47
%S 0,1,17,37,77,197,513,993,1837,2617,2637,4097,5437,65537,261633,
%T 364137,437837,2097153,16777217,32761917,54644032237,68719476737,
%U 137438953473,1099511627777
%N Numbers k such that k^2 + 1 divides 2^k + 8.
%C Prime terms are 17, 37, 197, 2617, 5437, 65537, 437837, ...
%C Numbers t such that 2^t + 1 is a term are 4, 9, 12, 16, 21, 24, 36, 37, 40, 45, 49, 52, 57, 64, 69, 76, 84, 96, ...
%t Select[Range[0, 9999], Divisible[2^# + 8, #^2 + 1] &] (* _Alonso del Arte_, Sep 16 2018 *)
%o (PARI) isok(n)=Mod(2, n^2+1)^n==-8;
%Y Cf. A247220, A319216, A319233.
%K nonn,more
%O 1,3
%A _Altug Alkan_, Sep 15 2018
%E a(21)-a(24) from _Hiroaki Yamanouchi_, Sep 16 2018