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

Author

N. J. A. Sloane, Sep 04 2004

Keywords

• nonn
• frac

Examples

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

References

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

Links

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

Crossrefs

Cf. A097917.

Programs

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

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

Extensions

More terms from Robin Visser, Feb 28 2024