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Nonsquares m such that the discriminant of the quadratic field Q(sqrt(m)) < m.
2

%I #13 Jun 24 2022 05:22:58

%S 18,20,27,32,45,48,50,52,54,63,68,72,75,80,84,90,96,98,99,108,112,116,

%T 117,125,126,128,132,135,147,148,150,153,160,162,164,171,175,176,180,

%U 189,192,198,200,207,208,212,216,224,228,234,240,242,243,244,245,250

%N Nonsquares m such that the discriminant of the quadratic field Q(sqrt(m)) < m.

%H Amiram Eldar, <a href="/A072904/b072904.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) appears to be asymptotic to C*n with C = 3.4... .

%t Select[Range[250], !IntegerQ@Sqrt[#] && NumberFieldDiscriminant[Sqrt[#]] < # &] (* _Amiram Eldar_, Jun 24 2022 *)

%o (PARI) isok(m) = !issquare(m) && (quaddisc(m) < m); \\ _Michel Marcus_, Feb 18 2021

%Y Cf. A037449.

%Y Intersection of A000037 and A072903.

%K easy,nonn

%O 1,1

%A _Benoit Cloitre_, Aug 10 2002

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Last modified September 20 02:18 EDT 2024. Contains 376016 sequences. (Running on oeis4.)