Search results
Results from the WOW.Com Content Network
Divisor functions were studied by Ramanujan, who gave a number of important congruences and identities; these are treated separately in the article Ramanujan's sum. A related function is the divisor summatory function, which, as the name implies, is a sum over the divisor function.
In number theory, the divisor summatory function is a function that is a sum over the divisor function. It frequently occurs in the study of the asymptotic behaviour of the Riemann zeta function . The various studies of the behaviour of the divisor function are sometimes called divisor problems .
Particular examples of k-periodic number theoretic functions are the Dirichlet characters = modulo k and the greatest common divisor function () = (,). It is known that every k-periodic arithmetic function has a representation as a finite discrete Fourier series of the form
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. Arithmetic functions are often extremely irregular (see table ), but some of them have series expansions in terms of Ramanujan's sum .
Pages in category "Divisor function" The following 28 pages are in this category, out of 28 total. This list may not reflect recent changes. ...
Divisor function d(n) up to n = 250 Prime-power factors. In number theory, a superior highly composite number is a natural number which, in a particular rigorous sense, has many divisors. Particularly, it is defined by a ratio between the number of divisors an integer has and that integer raised to some positive power.
Multiplicative function; Additive function; Dirichlet convolution; Erdős–Kac theorem; Möbius function. Möbius inversion formula; Divisor function; Liouville function; Partition function (number theory) Integer partition; Bell numbers; Landau's function; Pentagonal number theorem; Bell series; Lambert series
Sigma function σ 1 (n) up to n = 250 Prime-power factors. In number theory, a colossally abundant number (sometimes abbreviated as CA) is a natural number that, in a particular, rigorous sense, has many divisors. Particularly, it is defined by a ratio between the sum of an integer's divisors and that integer raised to a power higher than one ...