Exponential and Infinitary Divisors

Lelechenko, Andrew V.

doi:10.1007/s11253-017-1289-7

Ukr Math J

2017

DOI: 10.1007/s11253-017-1289-7

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Exponential and Infinitary Divisors

Andrew V. Lelechenko

Abstract: Abstract. Our paper is devoted to several problems from the field of modified divisors: namely exponential and infinitary divisors. We study the behaviour of modified divisors, sum-of-divisors and totient functions. Main results concern with the asymptotic behaviour of mean values and explicit estimates of extremal orders.

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2024

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Incidence Functions of the Exponential Divisor Poset

Haukkanen

2024

MathPann

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A positive integer is said to be an exponential divisor or an e-divisor of if 𝑑𝑖 ∣ 𝑛𝑖 for all prime divisors 𝑝𝑖 of 𝑛. In addition, 1 is an e-divisor of 1. It is easy to see that ℤ+ is a poset under the e-divisibility relation. Utilizing this observation we show that e-convolution of arithmetical functions is an example of the convolution of incidence functions of posets. We also note that the identity, units and the Möbius function are preserved in this process.

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Incidence Functions of the Exponential Divisor Poset

Haukkanen

2024

MathPann

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Exponential and Infinitary Divisors

Cited by 1 publication

References 13 publications

Incidence Functions of the Exponential Divisor Poset

Incidence Functions of the Exponential Divisor Poset

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