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On the Erdős primitive set conjecture in function fields
Andrés Gómez-Colunga, Charlotte Kavaler, Nathan McNew +1
Erdős proved that converges for any primitive set of integers and later conjectured this sum is maximized when is the se…
On the size of primitive sets in function fields
Andrés Gómez-Colunga, Charlotte Kavaler, Nathan McNew +1
A set is primitive if no element of the set divides another. We consider primitive sets of monic polynomials over a finite field and find natural generalizations of many of the res…
Primitive and geometric-progression-free sets without large gaps
Nathan McNew
We prove the existence of primitive sets (sets of integers in which no element divides another) in which the gap between any two consecutive terms is substantially smaller than the…
Counting primitive subsets and other statistics of the divisor graph of
Nathan McNew
Let denote the count of the primitive subsets of the integers . We give a new proof that which allows us to give a good error term an…
Popular values of the largest prime divisor function
Nathan McNew
We consider the distribution of the largest prime divisor of the integers in the interval , and investigate in particular the mode of this distribution, the prime number(s)…