Multiplicative Number Theory

Building on its broad strengths in mathematics in general, and in special functions in particular, the Wolfram Language provides a unique level of support for multiplicative number theory, including not only highly general function evaluation, but also symbolic simplification.

(OrangeLink[Zeta Functions », paclet:guide/ZetaFunctionsAndPolylogarithms])

(RefLink[Zeta, paclet:ref/Zeta]) — Riemann zeta function

Dirichlet Series

(RefLink[DirichletL, paclet:ref/DirichletL]) — Dirichlet L-functions

(RefLink[DirichletTransform, paclet:ref/DirichletTransform]) — Dirichlet transform of an arbitrary sequence

(OrangeLink[Arithmetic Functions », paclet:guide/NumberTheoreticFunctions])

(RefLink[DirichletCharacter, paclet:ref/DirichletCharacter]) — Dirichlet character

(RefLink[DivisorSigma, paclet:ref/DivisorSigma]) — divisor-sum function

(OrangeLink[Prime Numbers », paclet:guide/PrimeNumbers])

(RefLink[PrimePi, paclet:ref/PrimePi]) — the number of primes up to n

(RefLink[PrimeNu, paclet:ref/PrimeNu]) — the number of distinct primes in the factorization of n

(RefLink[PrimeOmega, paclet:ref/PrimeOmega]) — the number of primes in the factorization of n

Perfect Numbers

(RefLink[PerfectNumber, paclet:ref/PerfectNumber]) — n(^th) perfect number

Operations

(RefLink[DivisorSum, paclet:ref/DivisorSum]) — compute a sum over divisors

(RefLink[DirichletConvolve, paclet:ref/DirichletConvolve]) — Dirichlet convolution of sequences