논문KCI 등재
Cesaro’s Formula in an Algebraic Setting
경북대학교 자연과학대학 수학과|2025.03|Kyungpook Mathematical Journal|제65권 제1호|pp. 15-23|DOI 10.5666/KMJ.2025.65.1.15
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
주제분류수학
초록
Let τ(n) denote the number of positive divisors of n. Cesaro’s formula says that the number of ordered pairs ⟨a,b⟩ of integers such that 1 ≤ a,b ≤ n and [a,b] = n is equal to τ(n2), where [a,b] is the least common multiple of a and b. We explain this result and related results in terms of a finite commutative semigroup of idempotents.
Abstract
Let τ(n) denote the number of positive divisors of n. Cesaro’s formula says that the number of ordered pairs ⟨a,b⟩ of integers such that 1 ≤ a,b ≤ n and [a,b] = n is equal to τ(n2), where [a,b] is the least common multiple of a and b. We explain this result and related results in terms of a finite commutative semigroup of idempotents.
관련 논문AI추천
Ideals of the Multiplicative Semigroups Zn and their ProductsJintana Sanwong, Wattapong Puninagool경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2009 · 제49권 제1호Counting subrings of the ring $\mathbb Z_m \times \mathbb Z_n$Laszlo Toth대한수학회 · 대한수학회지2019 · 제56권 제6호Unitary analogues of a generalized number-theoretic sumBoonrod Yuttanan, Traiwat Intarawong대한수학회 · 대한수학회논문집2023 · 제38권 제2호Factorizations into irreducible numerical semigroupsPedro A. Garcıa-Sanchez대한수학회 · 대한수학회논문집2025 · 제40권 제3호Generalizations of number-theoretic sumsNarakorn Rompurk Kanasri, Patchara Pornsurat, Yanapat Tongron대한수학회 · 대한수학회논문집2019 · 제34권 제4호Note on Some Identities Involving Mobius FunctionVassilev-Missana장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2010 · 제13권 제1호
이 간행물의 다른 논문 (11건)
Totally Principal Ideal RingsEvangelina Santos, Farah Omar, Pascual Jarapp. 1-13Comments on "Regularity of a Particular Subsemigroup of the Semigroup of Transformations Preserving an Equivalence"Mosarof Sarkar, Shubh Narayan Singhpp. 25-28On completely inverse AG**-GroupoidsAdrian Naço, Kostaq Hila, Rigena Semapp. 29-36Determining the Solutions of General Quadratic Differential Equations Generated by q-ShiftJhuma Sarkar, Abhijit Banerjeepp. 37-51Cross-Gram Matrix and Riesz Sequences in Hilbert SpacesHamid Rezaei, Zahra Saeedipp. 53-61