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A146209 Integers a(n) for which the factorization in the real quadratic field Q(sqrt(a(n))) is not unique. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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
REFERENCES
Z. I. Borevich and I. R. Shafarevich, Zahlentheorie. Birkhäuser Verlag, Basel und Stuttgart (1966).
LINKS
EXAMPLE
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.
MATHEMATICA
Select[Range[200], SquareFreeQ[#] && NumberFieldClassNumber[Sqrt[#]] > 1 &] (* Alonso del Arte, Sep 05 2012 *)
CROSSREFS
Cf. A003172.
Sequence in context: A001750 A231643 A276541 * A029702 A053330 A051990
KEYWORD
nonn
AUTHOR
Pahikkala Jussi, Oct 28 2008
STATUS
approved

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Last modified July 19 19:39 EDT 2024. Contains 374436 sequences. (Running on oeis4.)