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%I #16 May 18 2021 04:07:38
%S 148,229,257,316,321,404,469,473,564,568,592,621,733,756,761,788,837,
%T 892,916,993,1016,1028,1076,1101,1229,1257,1264,1284,1304,1332,1373,
%U 1396,1436,1489,1492,1509,1524,1556,1573,1593,1616,1620,1772,1876,1892,1901,1929,1944
%N Positive discriminants of orders with class number 3.
%C Also positive discriminants of orders with class group isomorphic to C_3.
%C The fundamental terms are listed in A094612.
%C It seems that for most k in this sequence, 4*k is also in this sequence. The smallest k such that this is not true is k = 564.
%C Conjecture: if a term k is congruent to 4 modulo 16, then k/4 is either here or in A133315; if a term k is congruent to 0 modulo 16, then k/4 is in this sequence.
%C Conjecture: a term k is in A006832 if and only if k/4 is not in this sequence.
%H Jianing Song, <a href="/A344409/b344409.txt">Table of n, a(n) for n = 1..10001</a>
%o (PARI) isA344409(d) = (d>0) && !issquare(d) && ((d%4==0)||(d%4==1)) && quadclassunit(d)[2]==[3]
%Y Cf. A133315 (positive discriminants of orders with class number 1), A344408 (class number 2), this sequence (class number 3).
%Y Cf. A328825 (the negative discriminant case), A094612, A006832.
%K nonn
%O 1,1
%A _Jianing Song_, May 17 2021
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