2 citations · 9 across the 9 of their papers we have counts for
10 papers
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…
Ramanujan, Robin, Highly Composite Numbers, and the Riemann Hypothesis
Jean-Louis Nicolas, Jonathan Sondow
We provide an historical account of equivalent conditions for the Riemann Hypothesis arising from the work of Ramanujan and, later, Guy Robin on generalized highly composite number…
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 …