A097917 Denominator of 2*zeta_K(-1) where K is the totally real field Q(sqrt(n)), as n runs through the squarefree numbers.

6, 3, 15, 1, 3, 3, 3, 3, 3, 1, 3, 3, 3, 3, 3, 3, 1, 3, 3, 1, 3, 3, 3, 3, 3, 3, 1, 1, 3, 3, 1, 3, 3, 3, 1, 3, 3, 1, 3, 3, 1, 1, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 3, 1, 3, 3, 1, 3, 3, 3, 3, 3, 1, 1, 1, 3, 1, 3, 3, 1, 1, 3, 3, 3, 1, 1, 3, 3, 3, 1, 3, 3, 1, 3, 1, 1, 1, 3, 3, 3, 3, 1, 3, 3, 3, 3

Offset

1,1

References

F. Hirzebruch, Hilbert modular surfaces, Ges. Abh. II, 225-323.

Links

Table of n, a(n) for n=1..96.

F. Hirzebruch, Hilbert modular surfaces, L'Enseignement Math., 19 (1973), 183-281. See p. 200.

Example

1/6, 1/3, 1/15, 1, 4/3, 7/3, 7/3, 1/3, 10/3, 4, ...

Prog

(Sage) [(round(60*QuadraticField(d).zeta_function(100)(-1).real())/30).denominator() for d in range(2, 100) if Integer(d).is_squarefree()]  # Robin Visser, Feb 28 2024
(PARI)
z(d) = -(1/2)*bernfrac(2)*d*sum(k=1, d-1, kronecker(d, k)*subst(bernpol(2), x, k/d)*(-1/2))
{v=[]; for(k=2, 100, if(issquarefree(k), my(d=k); if(k%4 <> 1, d = 4*k); v=concat(v, denominator(2*z(d)) ))); v} \\ Thomas Scheuerle, Feb 28 2024

Crossrefs

Cf. A097916.

Sequence in context: A345056 A049784 A341746 * A116570 A335567 A362625

Adjacent sequences: A097914 A097915 A097916 * A097918 A097919 A097920

Keyword

nonn,frac

Author

N. J. A. Sloane, Sep 04 2004

Extensions

More terms from Robin Visser, Feb 28 2024

Status

approved