ln(x) or loge(x). In number theory, an arithmetic, arithmetical, or number-theoretic function is generally any function whose domain is the set of positive...

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

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...

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

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...

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

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

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...

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

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

In number theory, a multiplicative function is an arithmetic function f {\displaystyle f} of a positive integer n {\displaystyle n} with the property that...

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

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

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 )...

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...

(t)}{t\log ^{2}(t)}}\mathrm {d} t.} Formulas for prime-counting functions come in two kinds: arithmetic formulas and analytic formulas. Analytic formulas for prime-counting...

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

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...

errors in mathematical computation by computing function bounds. Numerical methods involving interval arithmetic can guarantee relatively reliable and mathematically...

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

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

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

Integer function may refer to: Integer-valued function, an integer function Floor function, sometimes referred as the integer function, INT Arithmetic function...

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...

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...

mathematics, modular arithmetic is a system of arithmetic operations for integers, other than the usual ones from elementary arithmetic, where numbers "wrap...

In mathematics and statistics, the arithmetic mean ( /ˌærɪθˈmɛtɪk/ arr-ith-MET-ik), arithmetic average, or just the mean or average (when the context...

sum of an arithmetic function, by means of an inverse Mellin transform. Let { a ( n ) } {\displaystyle \{a(n)\}} be an arithmetic function, and let g...

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

arithmetic function over the divisors of a natural number n {\displaystyle n} , or equivalently the Dirichlet convolution of an arithmetic function f...