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%I #15 Jul 05 2017 15:14:12
%S 1,37,325,577,1297,2917,3601,4357,7057,8101,9217,14401,15877,22501,
%T 24337,28225,32401,41617,44101,46657,57601,60517,69697,72901,79525,
%U 86437,90001,93637,108901,133957,147457,156817,176401,197137,202501,219025,224677,236197,291601,298117,318097
%N Löschian numbers (A003136) of the form k^2+1.
%C Intersection of A002522 and A003136.
%C Corresponding values of k are 0, 6, 18, 24, 36, 54, 60, 66, 84, 90, 96, 120, 126, 150, 156, 168, 180, 204, 210, 216, 240, 246, 264, 270, 282, 294, 300, 306, ...
%H Charles R Greathouse IV, <a href="/A271184/b271184.txt">Table of n, a(n) for n = 1..10000</a>
%e 37 is a term because 37 = 6^2 + 1 = 4^2 + 4*3 + 3^2.
%t Select[Range[10^6], And[IntegerQ@Sqrt[# - 1], Resolve[Exists[{x, y}, Reduce[# == x^2 + x y + y^2, {x, y}, Integers]]]] &] (* _Michael De Vlieger_, Apr 01 2016 *)
%o (PARI) is(n) = #bnfisintnorm(bnfinit(z^2+z+1), n);
%o for(k=0, 2000, if(is(n=k^2+1), print1(n, ", ")));
%Y Cf. A002522, A003136.
%K nonn
%O 1,2
%A _Altug Alkan_, Apr 01 2016
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