A319983 -id:A319983

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A317987

Discriminants of orders of imaginary quadratic fields with 2 classes per genus, negated.

+10
4

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

1,1

COMMENTS

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.

LINKS

Jianing Song, Table of n, a(n) for n = 1..324

Rick L. Shepherd, Binary quadratic forms and genus theory, Master of Arts Thesis, University of North Carolina at Greensboro, 2013.

FORMULA

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.

PROG

(PARI) isA317987(n) = (-n)%4 < 2 && 2^(1+#quadclassunit(-n)[2])==quadclassunit(-n)[1]

CROSSREFS

Cf. A003171, A133676.

Fundamental terms are listed in A319983.

KEYWORD

nonn,fini

AUTHOR

Jianing Song, Oct 02 2018

STATUS

approved

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