

A344409


Positive discriminants of orders with class number 3.


2



148, 229, 257, 316, 321, 404, 469, 473, 564, 568, 592, 621, 733, 756, 761, 788, 837, 892, 916, 993, 1016, 1028, 1076, 1101, 1229, 1257, 1264, 1284, 1304, 1332, 1373, 1396, 1436, 1489, 1492, 1509, 1524, 1556, 1573, 1593, 1616, 1620, 1772, 1876, 1892, 1901, 1929, 1944
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Also positive discriminants of orders with class group isomorphic to C_3.
The fundamental terms are listed in A094612.
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.
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.
Conjecture: a term k is in A006832 if and only if k/4 is not in this sequence.


LINKS



PROG

(PARI) isA344409(d) = (d>0) && !issquare(d) && ((d%4==0)(d%4==1)) && quadclassunit(d)[2]==[3]


CROSSREFS

Cf. A133315 (positive discriminants of orders with class number 1), A344408 (class number 2), this sequence (class number 3).


KEYWORD

nonn


AUTHOR



STATUS

approved



