Asymptotic distribution of integers with certain prime factorizations

作者：Vernaeve Hans; Vindas Jasson^*; Weiermann Andreas

来源：Journal of Number Theory, 2014, 136: 87-99.

DOI：10.1016/j.jnt.2013.09.001

• Strong asymptotics for partition problems
• Matula numbers
• Rooted trees
• Tree enumeration by prime
• factorization

Let pi. < p2 < center dot center dot center dot < pv < center dot center dot center dot be the sequence of prime numbers and let m be a positive integer. We give a strong asymptotic formula for the distribution of the set of integers having prime factorizations of the form pm(k1) Pm(k)2 center dot center dot center dot pm(k)n with k1 <= k2 <= center dot center dot center dot <= kn. Such integers originate in various combinatorial counting problems; when m = 2, they arise as Matula numbers of certain rooted trees.

• 出版日期2014-3