A055110 -id:A055110

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A046085

Numbers n such that Q(sqrt(-n)) has class number 4.

+10
6

14, 17, 21, 30, 33, 34, 39, 42, 46, 55, 57, 70, 73, 78, 82, 85, 93, 97, 102, 130, 133, 142, 155, 177, 190, 193, 195, 203, 219, 253, 259, 291, 323, 355, 435, 483, 555, 595, 627, 667, 715, 723, 763, 795, 955, 1003, 1027, 1227, 1243, 1387, 1411, 1435, 1507, 1555

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Contains 54 numbers [Arno, Theorem 7], ..., 1387, 1411, 1435, 1507 and 1555. [R. J. Mathar, May 01 2010]

LINKS

Table of n, a(n) for n=1..54.

Steven Arno, The imaginary quadratic fields of class number 4, Acta Arithm. vol 60 issue 4 (1991).

Steven Arno, M. L. Robinson, Ferrell S. Wheeler, Imaginary quadratic fields with small odd class number, Acta Arith. 83 (1998) 295-330.

Keith Matthews, Tables of imaginary quadratic fields with small class numbers

Eric Weisstein's World of Mathematics, Pythagorean Triple.

Index entries for sequences related to quadratic fields

PROG

(PARI) \\ See A005847

CROSSREFS

See A003173, A005847, A006203, A046085, A046002, A055109, A046004, A055110, A046006, A055111 for class numbers 1 through 10.

KEYWORD

nonn,fini,full,changed

AUTHOR

N. J. A. Sloane, Jun 16 2000

STATUS

approved

A055109

Numbers k such that Q(sqrt(-k)) has class number 6.

+10
5

26, 29, 38, 53, 61, 87, 106, 109, 118, 157, 202, 214, 247, 262, 277, 298, 339, 358, 397, 411, 451, 515, 707, 771, 835, 843, 1059, 1099, 1147, 1203, 1219, 1267, 1315, 1347, 1363, 1563, 1603, 1843, 1915, 1963, 2227, 2283, 2443, 2515, 2563, 2787

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Jinyuan Wang, Table of n, a(n) for n = 1..51

Index entries for sequences related to quadratic fields

MATHEMATICA

Select[Range[10000], MoebiusMu[#] != 0 && NumberFieldClassNumber[Sqrt[-#]] == 6 &] (* Jinyuan Wang, Mar 08 2020 *)

PROG

(PARI) \\ See A005847.

CROSSREFS

See A003173, A005847, A006203, A046085, A046002, A055109, A046004, A055110, A046006, A055111 for class numbers 1 through 10.

KEYWORD

nonn,fini,full

AUTHOR

N. J. A. Sloane, Jun 16 2000

STATUS

approved

A055111

Numbers k such that Q(sqrt(-k)) has class number 10.

+10
5

74, 86, 119, 122, 143, 159, 166, 181, 197, 218, 229, 303, 317, 319, 346, 373, 394, 415, 421, 422, 538, 541, 611, 613, 635, 694, 699, 709, 757, 779, 803, 851, 853, 877, 923, 982, 1093, 1115, 1213, 1318, 1643, 1707, 1779, 1819, 1835, 1891, 1923

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Jinyuan Wang, Table of n, a(n) for n = 1..87

Index entries for sequences related to quadratic fields

MATHEMATICA

Select[Range[10000], MoebiusMu[#] != 0 && NumberFieldClassNumber[Sqrt[-#]] == 10 &] (* Jinyuan Wang, Mar 08 2020 *)

PROG

(PARI) \\ See A005847.

CROSSREFS

See A003173, A005847, A006203, A046085, A046002, A055109, A046004, A055110, A046006, A055111 for class numbers 1 through 10.

KEYWORD

nonn,fini,full

AUTHOR

N. J. A. Sloane, Jun 16 2000

STATUS

approved

A191411

Class number, k, of n; i.e., imaginary quadratic fields negated Q(sqrt(-n))=k, or 0 if n is not squarefree (A005117).

+10
0

1, 1, 1, 0, 2, 2, 1, 0, 0, 2, 1, 0, 2, 4, 2, 0, 4, 0, 1, 0, 4, 2, 3, 0, 0, 6, 0, 0, 6, 4, 3, 0, 4, 4, 2, 0, 2, 6, 4, 0, 8, 4, 1, 0, 0, 4, 5, 0, 0, 0, 2, 0, 6, 0, 4, 0, 4, 2, 3, 0, 6, 8, 0, 0, 8, 8, 1, 0, 8, 4, 7, 0, 4, 10, 0, 0, 8, 4, 5, 0, 0, 4, 3, 0, 4, 10, 6, 0, 12, 0, 2, 0, 4, 8, 8, 0, 4, 0, 0, 0, 14, 4, 5, 0, 8

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,5

LINKS

Table of n, a(n) for n=1..105.

Eric Weisstein's World of Mathematics, Class Number

Index entries for sequences related to quadratic fields

MATHEMATICA

f[n_] := If[! SquareFreeQ@ n, 0, NumberFieldClassNumber@Sqrt@ -n]; Array[f, 105]

PROG

(PARI) a(n) = if (! issquarefree(n), 0, qfbclassno(-n*if((-n)%4>1, 4, 1))); \\ Michel Marcus, Jul 08 2015

CROSSREFS

a(n)= 0: A013929; a(n)= 1: A003173; a(n)= 2: A005847; a(n)= 3: A006203; a(n)= 4: A046085; a(n)= 5: A046002; a(n)= 6: A055109; a(n)= 7: A046004; a(n)= 8: A055110; a(n)= 9: A046006; a(n)=10: A055111; a(n)=11: A046008; a(n)=12: n/a;

a(n)=13: A046010; a(n)=14: n/a; a(n)=15: A046012; a(n)=16: n/a; a(n)=17: A046014; a(n)=18: n/a; a(n)=19: A046016;

a(n)=20: n/a; a(n)=21: A046018; a(n)=22: n/a;

a(n)=23: A046020; a(n)=24: n/a; a(n)=25: A056987; etc.

Cf. A191408, A191410.

Cf. A000924 (without the zeros).

KEYWORD

easy,nonn,changed

AUTHOR

Robert G. Wilson v, Jun 01 2011

STATUS

approved

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