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%I #16 Feb 29 2024 08:54:03
%S 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,
%T 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,
%U 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
%N Denominator of 2*zeta_K(-1) where K is the totally real field Q(sqrt(n)), as n runs through the squarefree numbers.
%D F. Hirzebruch, Hilbert modular surfaces, Ges. Abh. II, 225-323.
%H F. Hirzebruch, <a href="http://www.maths.ed.ac.uk/~v1ranick/papers/hirzhilb.pdf">Hilbert modular surfaces</a>, L'Enseignement Math., 19 (1973), 183-281. See p. 200.
%e 1/6, 1/3, 1/15, 1, 4/3, 7/3, 7/3, 1/3, 10/3, 4, ...
%o (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
%o (PARI)
%o z(d) = -(1/2)*bernfrac(2)*d*sum(k=1, d-1, kronecker(d, k)*subst(bernpol(2), x, k/d)*(-1/2))
%o {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
%Y Cf. A097916.
%K nonn,frac
%O 1,1
%A _N. J. A. Sloane_, Sep 04 2004
%E More terms from _Robin Visser_, Feb 28 2024
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