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## Displaying 1 – 15 of 15

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Integers

### Abundancy “outlaws” of the form $\frac{\left(\sigma \left(N\right)+t\right)}{N}$.

Journal of Integer Sequences [electronic only]

### Berechnung der Menge von Primzahlen, welche innerhalb der ersten Milliarde natürlicher Zahlen vorkommen

Mathematische Annalen

### CM liftings of supersingular elliptic curves

Journal de Théorie des Nombres de Bordeaux

Assuming GRH, we present an algorithm which inputs a prime $p$ and outputs the set of fundamental discriminants $D<0$ such that the reduction map modulo a prime above $p$ from elliptic curves with CM by ${𝒪}_{D}$ to supersingular elliptic curves in characteristic $p$ is surjective. In the algorithm we first determine an explicit constant ${D}_{p}$ so that $|D|>{D}_{p}$ implies that the map is necessarily surjective and then we compute explicitly the cases $|D|<{D}_{p}$.

### Computing the summation of the Möbius function.

Experimental Mathematics

Acta Arithmetica

### Generalized perfect numbers.

Acta Universitatis Sapientiae. Mathematica

### Iterating the sum-of-divisors function.

Experimental Mathematics

### Jumping champions.

Experimental Mathematics

### Landau’s function for one million billions

Journal de Théorie des Nombres de Bordeaux

Let ${𝔖}_{n}$ denote the symmetric group with $n$ letters, and $g\left(n\right)$ the maximal order of an element of ${𝔖}_{n}$. If the standard factorization of $M$ into primes is $M={q}_{1}^{{\alpha }_{1}}{q}_{2}^{{\alpha }_{2}}...{q}_{k}^{{\alpha }_{k}}$, we define $\ell \left(M\right)$ to be ${q}_{1}^{{\alpha }_{1}}+{q}_{2}^{{\alpha }_{2}}+...+{q}_{k}^{{\alpha }_{k}}$; one century ago, E. Landau proved that $g\left(n\right)={max}_{\ell \left(M\right)\le n}M$ and that, when $n$ goes to infinity, $logg\left(n\right)\sim \sqrt{nlog\left(n\right)}$.There exists a basic algorithm to compute $g\left(n\right)$ for $1\le n\le N$; its running time is $𝒪\left({N}^{3/2}/\sqrt{logN}\right)$ and the needed memory is $𝒪\left(N\right)$; it allows computing $g\left(n\right)$ up to, say, one million. We describe an algorithm to calculate $g\left(n\right)$ for $n$ up to ${10}^{15}$. The main idea is to use the so-called $\ell$-superchampion...

Acta Arithmetica

### On the distribution of analytic $\sqrt{|\text{Sh}|}$ values on quadratic twists of elliptic curves.

Experimental Mathematics

### Properties of some functions connected to prime numbers.

JIPAM. Journal of Inequalities in Pure &amp; Applied Mathematics [electronic only]

### The unitary amicable pairs to ${10}^{8}$.

International Journal of Mathematics and Mathematical Sciences

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