Year: 2026
Type: article
Abstract: For a prime p, let vp(n!) denote the exponent of p in the prime factorization of n!.Starting from the digital identity vp(n!) = (n -sp(n))/(p -1), where sp(n) is the sum of the base-p digits of n, we develop three results.First, we give two direct generating-function identities and derive an inhomogeneous Mahler-type functional equation for the ordinary generating function Hp(z) = ∑︁ n≥0 vp(n!)z n , obtaining from it an explicit iterated series expansion.Second, on each complete base-p block 0 ≤ n < p m , we determine an exact factorization for the generating polynomial ∑︁ 0≤n
Source: Discrete Mathematics Letters
Author: Armend Sh. Shabani
Institution: University of Prishtina
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7223549522