4 papers · 1 filter
On the number of divisors of Mersenne numbers
Vjekoslav KovaÄ, Florian Luca
Denote , where is the number of divisors function. Motivated by a question of Paul ErdÅs, we show that the sequence of ratios …
Lacunary sequences whose reciprocal sums represent all rational numbers in an interval
Wouter van Doorn, Vjekoslav KovaÄ
Disproving a conjecture of Bleicher and ErdÅs, we show that there exists a lacunary sequence of positive integers such that finite sums of reciprocals of its terms attain all rati…
On several irrationality problems for Ahmes series
Vjekoslav KovaÄ, Terence Tao
Using basic tools of mathematical analysis and elementary probability theory we address several problems on the irrationality of series of distinct unit fractions, .…
On the irrationality of certain super-polynomially decaying series
TonÄi CrmariÄ, Vjekoslav KovaÄ
We give a negative answer to a question by Paul ErdÅs and Ronald Graham on whether the series \[ \sum_{n=1}^{\infty} \frac{1}{(n+1)(n+2)\cdots(n+f(n))} \] has an irrational sum wh…