Arithmetic function

In number theory, an arithmetic, arithmetical, or number-theoretic function is for most authors any function f(n) whose domain is the positive integers and whose range is a subset of the complex numbers. Hardy & Wright include in their definition the requirement that an arithmetical function "expresses some arithmetical property of n". An example of an arithmetic function is the divisor function whose value at a positive integer n is equal to the number of divisors of n. There is a larger class of number-theoretic functions that do not fit the above definition, e.g. the prime-counting functions. This article provides links to functions of both classes. Many of the functions mentioned in this article have expansions as series involving these sums; see the article Ramanujan's sum for examples.

Words

This table shows the example usage of word lists for keywords extraction from the text above.

WordWord FrequencyNumber of ArticlesRelevance
arithmetical4800.328
function7221220.284
number-theoretic3170.28
arithmetic414430.243
functions5181730.21

This website uses cookies to ensure you get the best experience on our website. Learn more. Got it.