2 citations · 9 across the 9 of their papers we have counts for
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The Landau function and the Riemann Hypothesis
Marc Deleglise, Jean-Louis Nicolas
The Landau function is the maximal order of an element of the symmetric group of degree ; it is also the largest product of powers of primes whose sum is . The mai…
On Landau's function g(n)
Jean-Louis Nicolas
Let be the symmetric group of letters; Landau considered the function defined as the maximal order of an element of . This function is non-decreasing. Let us…
Maximal product of primes whose sum is bounded
Marc Deléglise, Jean-Louis Nicolas
If n is a positive integer, let h(n) denote the maximal value of the product of distinct primes whose sum does not exceed n. We give some properties of this function h and describe…
Small values of the Euler function and the Riemann hypothesis
Jean-Louis Nicolas
Let $\vfi$ be Euler's function, $\ga$ be Euler's constant and be the product of the first primes. In this article, we consider the function $c(n) =(n/\vfi(n)-e^\ga\log\lo…
On SA, CA, and GA numbers
Geoffrey Caveney, Jean-Louis Nicolas, Jonathan Sondow
Gronwall's function is defined for by where is the sum of the divisors of . We call an integer a \emph{GA1 number} if …
Robin's theorem, primes, and a new elementary reformulation of the Riemann Hypothesis
Geoffrey Caveney, Jean-Louis Nicolas, Jonathan Sondow
For n>1, let G(n)=σ(n)/(n log log n), where σ(n) is the sum of the divisors of n. We prove that the Riemann Hypothesis is true if and only if 4 is the only composite number N satis…