Büyükaşık, EnginGöral, HaydarSertbaş, Doğa Can2025-04-182025-04-182024Buyukasik, E., Goral, H., & Sertbas, D. C. (2024). A note on variants of Euler's φ-function.00333883http://dx.doi.org/10.5486/PMD.2024.9674https://hdl.handle.net/20.500.12713/6580It is well-known that the sum of the first n consecutive integers always divides the k-th power sum of the first n consecutive integers when k is odd. Motivated by this result, in this note, we study the divisibility properties of the power sum of positive integers that are coprime to n and not surpassing n. First, we prove a finiteness result for our divisibility sets using smooth numbers in short intervals. Then, we find the exact structure of a certain divisibility set that contains the orders of these power sums and our result is of computational flavour. © 2024 Institute of Mathematics, University of Debrecen. All rights resereninfo:eu-repo/semantics/closedAccessBernoulli NumbersEuler’s φ-functionPrime Number TheoryArticle1051-26789WOS:0013030461000052-s2.0-85199537363Q310.5486/PMD.2024.9674Q3