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Reticuloendotheliosis and Lymphoproliferative Disease
Retrovirus-induced tumors, specifically reticuloendotheliosis (RE) and lymphoproliferative disease (LPD), are the most common virus-induced tumors in...
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On a group-theoretical generalization of the Gauss formula
We discuss a group-theoretical generalization of the well-known Gauss formula involving the function that counts the number of automorphisms of a...
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On Ramanujan Sums over a Dedekind Domain with Finite Norm Property
In this paper, we consider Ramanujan’s sums over arbitrary Dedekind domain with finite norm property. We define the Ramanujan’s sums η ( a , A ) and η ( B , A ...
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Sign changes of certain arithmetical function at prime powers
We examine an arithmetical function defined by recursion relations on the sequence { f ( p k )} k ∈ℕ and obtain sufficient condition(s) for the sequence to...
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A Menon-type identity using Klee’s function
Menon’s identity is a classical identity involving gcd sums and the Euler totient function φ . A natural generalization of φ is the Klee’s function Φ s ....
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Combinations of Ranks and Cranks of Partitions Moduli 6, 9 and 12 and Their Comparison with the Partition Function
Let L \(\epsilon\) {6, 9, 12}. We determine the generating...
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Integer factorization and finite Fourier series expansion
Given two integers a and k > 0, the number of factorizations of a (mod k ) is the number of ordered pairs ( s, t ) ∈ {0 , 1 , . . . , k − 1} 2 satisfying s...
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Another regular Menon-type identity in residually finite Dedekind domains
We give a regular extension of the Menon-type identity to residually finite Dedekind domains.
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Evaluation of ecotoxicological and chemical properties of soil amended with Hudson River (New York, USA) sediment
The aim of this study was to assess the potential for application of Hudson River sediment as a plant growth medium by mixing with various...
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Inequalities for weighted sums of Mertens functions
In this article we derive some polynomial inequalities for Mertens functions.
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Lucas numbers as sums of two repdigits
In this paper, we determine all Lucas numbers that are sums of two repdigits. The largest one is L 14 = 843 = 66 + 777.
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On a sequence formed by iterating a divisor operator
Let ℕ be the set of positive integers and let s ∈ ℕ. We denote by d s the arithmetic function given by d s ( n ) = ( d ( n )) s , where d ( n ) is the number of...
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Independence of additive, multiplicative, exponential and logarithmic functions
The independence of four types of functions, namely, additive, multiplicative, exponential and logarithmic functions defined over two types of...