A029703 -id:A029703 - cp's OEIS frontend

A029702 Q(sqrt(n)) has class number 2.

10, 15, 26, 30, 34, 35, 39, 42, 51, 55, 58, 65, 66, 70, 74, 78, 85, 87, 91, 95, 102, 105, 106, 110, 111, 114, 115, 119, 122, 123, 138, 143, 146, 154, 155, 159, 165, 174, 178, 182, 183, 185, 186, 187, 190, 194, 202, 203, 205, 215, 218, 221, 222, 230, 238, 246

Offset: 1

Paolo Dominici (pl.dm(AT)libero.it)

nonn

Smallest term that is in A146209 but not this sequence is 79, since Q(sqrt(79)) has class number 3. - Alonso del Arte, Aug 25 2014

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Index entries for sequences related to quadratic fields

Cf. A003172, A029703-A029705, A218038-A218042.

Select[Range[246], SquareFreeQ[#] && NumberFieldClassNumber@Sqrt[#] == 2 &] (* Arkadiusz Wesolowski, Oct 22 2012 *)

A007947(n)={my(p); p=factor(n)[, 1]; prod(i=1, length(p), p[i]); }
{ for (n=2, 10^3,
    if ( n!=A007947(n), next() );
    K = bnfinit(x^2 - n);
    if ( K.cyc == [2], print1( n, ", ") );
); }
/* Joerg Arndt, Oct 18 2012 */

A029704 Q(sqrt(n)) has class number 4.

Original entry on oeis.org

82, 130, 145, 170, 195, 210, 219, 231, 255, 274, 290, 291, 322, 323, 330, 370, 390, 410, 434, 435, 438, 445, 455, 462, 483, 505, 510, 514, 530, 546, 555, 570, 579, 582, 595, 610, 615, 626, 627, 651, 658, 663, 674, 689, 690, 706, 714, 715, 723, 731, 754, 759, 770

Offset: 1

Paolo Dominici (pl.dm(AT)libero.it)

nonn

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Index entries for sequences related to quadratic fields

Cf. A003172, A029702-A029703, A029705, A218038-A218042.

Select[Range[770], SquareFreeQ[#] && NumberFieldClassNumber@Sqrt[#] == 4 &] (* Arkadiusz Wesolowski, Oct 18 2012 *)

is(n)=if(issquarefree(n), my(c=bnfinit('x^2-n).cyc); c==[4] || c==[2,2], 0) \\ Charles R Greathouse IV, Oct 18 2012

Initial term added by Arkadiusz Wesolowski, Oct 18 2012

A081363 Smallest squarefree integer k such that Q(sqrt(k)) has class number n.

Original entry on oeis.org

2, 10, 79, 82, 401, 235, 577, 226, 1129, 1111, 1297, 730, 4759, 1534, 9871, 2305, 7054, 4954, 15409, 3601, 7057, 4762, 23593, 9634, 24859, 13321, 8761, 5626, 49281, 11665, 97753, 15130, 55339, 19882, 25601, 18226, 24337, 19834, 41614, 16899, 55966, 47959

Offset: 1

Dean Hickerson, Mar 19 2003

nonn

What is known about the asymptotics of this sequence? - Charles R Greathouse IV, Jan 26 2017

Records: 2, 10, 79, 82, 401, 577, 1129, 1297, 4759, 9871, 15409, 23593, 24859, 49281, 97753, 106537, 159199, 197137, 212137, 239119, 245023, 444089, 589822, 614849, 815413, 837929, 943951, 1025494, 1224121, 1240369, 1333255, 1334026, ..., . - Robert G. Wilson v, Apr 12 2017

Robert G. Wilson v, Table of n, a(n) for n = 1..214

Cf. A081319, A081364, A094619, A094612, A094613, A094614.

Cf. A219361, A029702, A029703, A029704, A029705, A218038, A218039, A218040, A218041, A218042, A276541. - Robert G. Wilson v, Apr 12 2017

t[] := 0; k = 2; While[k < 56000, cn = NumberFieldClassNumber@Sqrt@k; If[ t[cn] == 0, t[cn] = k; Print[{cn, k}]]; k++]; t@# & /@ Range@ 42 (* _Robert G. Wilson v, Apr 12 2017 *)

v=vector(100); for(n=2,1e6, if(!issquarefree(n), next); t=qfbclassno(if(n%4>1,4*n,n)); if(t<=#v && v[t]==0, v[t]=n; print("a("t") = "n))) \\ Charles R Greathouse IV, Jan 26 2017

More terms from Max Alekseyev, Apr 28 2010

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A029702 Q(sqrt(n)) has class number 2.

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A029704 Q(sqrt(n)) has class number 4.

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A081363 Smallest squarefree integer k such that Q(sqrt(k)) has class number n.

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Author

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Mathematica

PARI

Extensions