A294795 Decimal expansion of the unique real number in [1, 2] satisfying ((2^x)/(2^x-1))*((3^x+1)/(3^x-1)) = zeta(x).

1, 8, 8, 7, 7, 9, 0, 9, 2, 6, 7, 0, 8, 1, 1, 8, 9, 2, 7, 1, 9, 6, 3, 2, 1, 5, 4, 2, 0, 3, 5, 1, 1, 6, 6, 6, 8, 2, 2, 3, 4, 7, 0, 1, 2, 6, 0, 2, 8, 0, 1, 6, 4, 7, 9, 8, 0, 9, 1, 5, 4, 3, 8, 0, 9, 5, 5, 4, 6, 7, 3, 4, 7, 1, 4, 4, 1, 5, 3, 3, 8, 1, 8, 8, 8, 1, 0, 8, 4, 2, 6, 6, 7

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

Table of n, a(n) for n=1..93.

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

Sequence in context: A329220 A127196 A350715 * A173623 A070481 A011109

Adjacent sequences: A294792 A294793 A294794 * A294796 A294797 A294798

Keyword

nonn,cons

Author

Michel Marcus, Nov 09 2017

Status

approved