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A317987
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Discriminants of orders of imaginary quadratic fields with 2 classes per genus, negated.
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4
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39, 55, 56, 63, 68, 80, 128, 136, 144, 155, 156, 171, 184, 196, 203, 208, 219, 220, 224, 252, 256, 259, 260, 264, 275, 276, 291, 292, 308, 320, 323, 328, 336, 355, 360, 363, 384, 387, 388, 400, 456, 468, 475, 504, 507, 528, 544, 552, 564, 568, 576, 580, 592, 600, 603, 612, 616, 624, 640
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OFFSET
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1,1
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COMMENTS
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k is a term iff the form class group of positive binary quadratic forms with discriminant -k is isomorphic to (C_2)^r X C_4.
This is a subsequence of A133676, so it's finite. It seems that this sequence has 324 terms, the largest being 87360.
The smallest number in A133676 but not here is 3600.
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LINKS
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FORMULA
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The form class groups of positive binary quadratic forms with discriminant -39, -55, -56, -63, -68, -80 and -128 are all isomorphic to C_4, so 39, 55, 56, 63, 68, 80 and 128 are all members of this sequence.
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PROG
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(PARI) isA317987(n) = (-n)%4 < 2 && 2^(1+#quadclassunit(-n)[2])==quadclassunit(-n)[1]
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CROSSREFS
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Fundamental terms are listed in A319983.
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KEYWORD
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nonn,fini
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AUTHOR
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STATUS
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approved
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