A146209 Integers a(n) for which the factorization in the real quadratic field Q(sqrt(a(n))) is not unique.

10, 15, 26, 30, 34, 35, 39, 42, 51, 55, 58, 65, 66, 70, 74, 78, 79, 82, 85, 87, 91, 95, 102, 105, 106, 110, 111, 114, 115, 119, 122, 123, 130, 138, 142, 143, 145, 146, 154, 155, 159, 165, 170, 174, 178, 182, 183, 185, 186, 187, 190, 194, 195

Offset: 1

Author

Pahikkala Jussi, Oct 28 2008

Keywords

• nonn

Comments

The class number of Q(sqrt(a(n))) is greater than 1.

Contains A029702, A053330 and A051990 as subsequences. See A219361 for positive integers D for which Q(sqrt D) is a UFD. - M. F. Hasler, Oct 30 2014

Examples

			For n = 6, a(6) = 35 since 35 is the sixth positive squarefree integer u for which the factorization in Q(sqrt(u)) is not unique.
		

References

• Z. I. Borevich and I. R. Shafarevich, Zahlentheorie. Birkhäuser Verlag, Basel und Stuttgart (1966).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A003172.

Programs

Mathematica

Select[Range[200], SquareFreeQ[#] && NumberFieldClassNumber[Sqrt[#]] > 1 &] (* Alonso del Arte, Sep 05 2012 *)