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A097916
Numerator of 2*zeta_K(-1) where K is the totally real field Q(sqrt(n)), as n runs through the squarefree numbers.
5
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
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
KEYWORD
nonn,frac
AUTHOR
N. J. A. Sloane, Sep 04 2004
EXTENSIONS
More terms from Robin Visser, Feb 28 2024
STATUS
approved