In number theory, an arithmetic, arithmetical, or number-theoretic function is generally any function f(n) whose domain is the positive integers and whose...

the OEIS). In number theory another arithmetic function closely related to the Möbius function is the Mertens function, defined by M ( n ) = ∑ k = 1 n μ...

elementary function arithmetic (EFA), also called elementary arithmetic and exponential function arithmetic, is the system of arithmetic with the usual...

In number theory, a multiplicative function is an arithmetic function f(n) of a positive integer n with the property that f(1) = 1 and f ( a b ) = f (...

multiplicative function (or totally multiplicative function) is an arithmetic function (that is, a function whose domain is the natural numbers), such that...

mathematics, the arithmetic zeta function is a zeta function associated with a scheme of finite type over integers. The arithmetic zeta function generalizes...

by sigma function one can mean one of the following: The sum-of-divisors function σa(n), an arithmetic function Weierstrass sigma function, related to...

an additive function is an arithmetic function f(n) of the positive integer variable n such that whenever a and b are coprime, the function applied to...

In mathematics, the fundamental theorem of arithmetic, also called the unique factorization theorem and prime factorization theorem, states that every...

In number theory, the gcd-sum function, also called Pillai's arithmetical function, is defined for every n {\displaystyle n} by P ( n ) = ∑ k = 1 n gcd...

In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus...

Fourier coefficients of the Ramanujan modular form Divisor function, an arithmetic function giving the number of divisors of an integer This disambiguation...

Mangoldt function is an arithmetic function named after German mathematician Hans von Mangoldt. It is an example of an important arithmetic function that...

Rational points can be directly characterized by height functions which measure their arithmetic complexity. The structure of algebraic varieties defined...

In number theory, the Lagarias arithmetic derivative or number derivative is a function defined for integers, based on prime factorization, by analogy...

quasi-arithmetic mean or generalised f-mean or Kolmogorov-Nagumo-de Finetti mean is one generalisation of the more familiar means such as the arithmetic mean...

classic Möbius inversion formula is a relation between pairs of arithmetic functions, each defined from the other by sums over divisors. It was introduced...

convolution (or divisor convolution) is a binary operation defined for arithmetic functions; it is important in number theory. It was developed by Peter Gustav...

Lamé function Mathieu function Mittag-Leffler function Painlevé transcendents Parabolic cylinder function Arithmetic–geometric mean Ackermann function: in...

arithmetic function is some simpler or better-understood function which takes the same values "on average". Let f {\displaystyle f} be an arithmetic function...

In number theory, the sum of squares function is an arithmetic function that gives the number of representations for a given positive integer n as the...

theory, a divisor function is an arithmetic function related to the divisors of an integer. When referred to as the divisor function, it counts the number...

is credited with discovering that the partition function has nontrivial patterns in modular arithmetic. For instance the number of partitions is divisible...

The Liouville lambda function, denoted by λ(n) and named after Joseph Liouville, is an important arithmetic function. Its value is +1 if n is the product...

arithmetic function is some simpler or better-understood function which "usually" takes the same or closely approximate values. Let f be a function on...

(n)}{n^{s}}}} where L(χ, s) is a Dirichlet L-function. If the arithmetic function f has a Dirichlet inverse function f − 1 ( n ) {\displaystyle f^{-1}(n)} ...

over the distinct prime numbers dividing n. (For notation, see Arithmetical function.) An equivalent formulation is φ ( n ) = p 1 k 1 − 1 ( p 1 − 1 )...

pure mathematics devoted primarily to the study of the integers and arithmetic functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics...

Arithmetic is an elementary branch of mathematics that studies numerical operations like addition, subtraction, multiplication, and division. In a wider...

an example of an arithmetic function. In this context it is usually denoted dn and called the prime difference function. The function is neither multiplicative...