number theory, an average order of an arithmetic function is some simpler or better-understood function which takes the same values "on average". Let f {\displaystyle...

In number theory, an arithmetic, arithmetical, or number-theoretic function is generally any function whose domain is the set of positive integers and...

In number theory, a normal order of an arithmetic function is some simpler or better-understood function which "usually" takes the same or closely approximate...

numbers is the arithmetic mean – the sum of the numbers divided by how many numbers are in the list. For example, the mean or average of the numbers 2...

extremal orders of an arithmetic function are best possible bounds of the given arithmetic function. Specifically, if f(n) is an arithmetic function and m(n)...

statistics, the arithmetic mean ( /ˌærɪθˈmɛtɪk/ arr-ith-MET-ik), arithmetic average, or just the mean or average is the sum of a collection of numbers divided...

} ⁠ of each number, finding the arithmetic mean of the logarithms, and then returning the result to linear scale using the exponential function ⁠ exp...

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...

the inequality of arithmetic and geometric means, or more briefly the AM–GM inequality, states that the arithmetic mean of a list of non-negative real...

some of the most interesting examples of such identities result when considering the average order summatory functions over an arithmetic function f (...

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...

analyses of financial data, a weighted moving average (WMA) has the specific meaning of weights that decrease in arithmetical progression. In an n-day WMA...

or uniformizing function: assigns to each set one of its elements. These properties concern how the function is affected by arithmetic operations on its...

positive arguments. The harmonic mean is the reciprocal of the arithmetic mean of the reciprocals of the numbers, that is, the generalized f-mean with f (...

geometric means. The arithmetic–geometric mean is used in fast algorithms for exponential, trigonometric functions, and other special functions, as well as some...

computing function bounds. Numerical methods involving interval arithmetic can guarantee relatively reliable and mathematically correct results. Instead of representing...

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

arithmetic scheme or a scheme of finite type over integers. The arithmetic zeta function of a regular connected equidimensional arithmetic scheme of Kronecker...

where the sum is over all positive divisors d of n, can be proven in several ways. (See Arithmetical function for notational conventions.) One proof is to...

many primes that are congruent to a modulo d. The numbers of the form a + nd form an arithmetic progression a ,   a + d ,   a + 2 d ,   a + 3 d ,   … ,...

contraharmonic mean of a set of positive real numbers is defined as the arithmetic mean of the squares of the numbers divided by the arithmetic mean of the numbers:...

is φ(n), where φ is Euler's totient function. Since the order of an element of a finite group divides the order of the group, λ(n) divides φ(n). The following...

relates to arithmetic data associated with an elliptic curve E over a number field K to the behaviour of the Hasse–Weil L-function L(E, s) of E at s = 1...

total number of prime factors with multiplicity (see arithmetic function). That is, if we have a prime factorization of n {\displaystyle n} of the form n...

product over the primes is a cyclotomic polynomial of p − k {\displaystyle p^{-k}} ), the arithmetic functions defined by J k ( n ) J 1 ( n ) {\displaystyle...

The arithmetic mean, also known as "arithmetic average", is the sum of the values divided by the number of values. The arithmetic mean of a set of numbers...

to form a single summary statistic. Common aggregate functions include: Average (i.e., arithmetic mean) Count Maximum Median Minimum Mode Range Sum Others...

saturation begins, the growth slows to linear (arithmetic), and at maturity, growth approaches the limit with an exponentially decaying gap, like the initial...

estimates the average order of the divisor function d(n) and Gauss's circle problem that estimates the average order of the number of representations of a number...