关于几类乘法函数

Pub Date : 2024-04-09 DOI:10.1007/s00010-024-01053-5

Pentti Haukkanen

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引用次数: 0

摘要

当 m 和 n 是同素数时，如果 \(f(1)=1\) 和 \(f(mn)=f(m)f(n)\) 是乘法函数，则算术函数 f 是乘法函数。我们研究了乘法函数的某些子类之间的联系，如强乘法函数、超乘法函数和 totients。除其他外，超乘法函数与图腾完全相同，强乘法函数与所谓的级图腾完全相同。所有这些函数都满足具有递归性质的算术等式。

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On some classes of multiplicative functions

An arithmetical function f is multiplicative if \(f(1)=1\) and \(f(mn)=f(m)f(n)\) whenever m and n are coprime. We study connections between certain subclasses of multiplicative functions, such as strongly multiplicative functions, over-multiplicative functions and totients. It appears, among others, that the over-multiplicative functions are exactly same as the totients and the strongly multiplicative functions are exactly same as the so-called level totients. All these functions satisfy nice arithmetical identities which are recursive in character.

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