OFFSET
1,2
COMMENTS
This constant is named the Defantstant by Zubrilina (see link).
See the Defant link for more explanations on this constant.
The set of numbers {sigma_{-r}(n) | n>=1}, where sigma_{-r}(n) = Sum_{d|n} d^(-r), is dense in [1, zeta(r)) if and only if r <= this constant (Defant, 2015). - Amiram Eldar, Sep 25 2022
LINKS
Colin Defant, On the Density of Ranges of Generalized Divisor Functions, Notes on Number Theory and Discrete Mathematics, Vol. 21, No. 3 (2015), pp. 80-87; arXiv preprint, arXiv:1506.05432 [math.NT], 2015.
Nina Zubrilina, On the Number of Connected Components of Ranges of Divisor Functions, arXiv:1711.02871 [math.NT], 2017.
EXAMPLE
1.8877909267081189271963215420351166682234701260280164798091543809554673...
MATHEMATICA
RealDigits[x /. FindRoot[2^x*(3^x + 1)/((2^x - 1)*(3^x - 1)) == Zeta[x], {x, 3/2}, WorkingPrecision -> 120]][[1]] (* Amiram Eldar, Sep 25 2022 *)
PROG
(PARI) solve(x=1.5, 2, 2^x*(3^x+1)/((2^x-1)*(3^x-1)) - zeta(x))
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Michel Marcus, Nov 09 2017
STATUS
approved