A081319 - OEIS

A081319

Smallest squarefree integer k such that Q(sqrt(-k)) has class number n, or 0 if no such k exists.

1, 5, 23, 14, 47, 26, 71, 41, 199, 74, 167, 89, 191, 101, 239, 146, 383, 293, 311, 194, 431, 269, 647, 329, 479, 314, 983, 341, 887, 461, 719, 446, 839, 614, 1031, 626, 1487, 1199, 1439, 689, 1151, 794, 1847, 854, 1319, 941, 3023, 1106, 1511, 1109, 1559

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OFFSET

1,2

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..4500

Duncan A. Buell, Small class numbers and extreme values of L-functions of quadratic fields, Math. Comp., 31 (1977), 786-796.

FORMULA

a(n) = A060649(n) for odd n > 1. For even n, assuming that A060649(n) > 0 and A344072(n/2) > 0, a(n) = min{A060649(n), A344072(n/2)/4}. - Jianing Song, May 08 2021

EXAMPLE

From Jianing Song, May 08 2021: (Start)

a(6) = min{A060649(6), A344072(3)/4} = min{87, 104/4} = 26.

a(12) = min{A060649(12), A344072(6)/4} = min{231, 356/4} = 89.

a(18) = min{A060649(12), A344072(9)/4} = min{335, 1172/4} = 293.

a(38) = min{A060649(38), A344072(19)/4} = min{1199, 4916/4} = 1199. (End)

MATHEMATICA

t[_] := 0; k = -1; While[k > -3100, a = NumberFieldClassNumber@Sqrt@k; If[t[a] == 0, t[a] = -k; Print[{a, -k}]]; k--]; t /@ Range@51 (* Robert G. Wilson v, Sep 25 2017 *)

CROSSREFS

Cf. A060649, A038552, A046125, A014602-A046020.

Sequence in context: A054415 A156328 A078190 * A177242 A233756 A002582

Adjacent sequences: A081316 A081317 A081318 * A081320 A081321 A081322

KEYWORD

nonn

AUTHOR

Dean Hickerson, Mar 18 2003

EXTENSIONS

Edited by Max Alekseyev, Apr 28 2010

Escape clause added by Jianing Song, May 08 2021

STATUS

approved