A097916 Numerator of 2*zeta_K(-1) where K is the totally real field Q(sqrt(n)), as n runs through the squarefree numbers.

1, 1, 1, 1, 4, 7, 7, 1, 10, 4, 2, 19, 2, 23, 20, 25, 1, 34, 40, 2, 46, 38, 5, 41, 52, 8, 18, 21, 74, 56, 26, 7, 92, 14, 33, 85, 11, 28, 16, 112, 41, 4, 134, 116, 22, 41, 4, 46, 56, 54, 43, 6, 155, 52, 26, 206, 6, 212, 172, 34, 19, 206, 76, 12, 87, 197, 9, 206, 244, 12, 88, 278, 277, 248

Offset

1,5

References

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

Links

Table of n, a(n) for n=1..74.

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).numerator() 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, numerator(2*z(d)) ))); v} \\ Thomas Scheuerle, Feb 28 2024

Crossrefs

Cf. A097917.

Sequence in context: A021681 A114490 A182997 * A176529 A086775 A132266

Adjacent sequences: A097913 A097914 A097915 * A097917 A097918 A097919

Keyword

nonn,frac

Author

N. J. A. Sloane, Sep 04 2004

Extensions

More terms from Robin Visser, Feb 28 2024

Status

approved