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.

Zeta Functions »

Zeta Riemann zeta function

ZetaZero  ▪  LogIntegral  ▪  RiemannSiegelZ  ▪  PrimeZetaP  ▪  ...

Dirichlet Series

DirichletL Dirichlet L-functions

DirichletTransform Dirichlet transform of an arbitrary sequence

Arithmetic Functions »

DirichletCharacter Dirichlet character

DivisorSigma divisor-sum function

Divisors  ▪  MoebiusMu  ▪  EulerPhi  ▪  ...

Prime Numbers »

PrimePi the number of primes up to

PrimeNu the number of distinct primes in the factorization of n

PrimeOmega the number of primes in the factorization of n

Prime  ▪  LiouvilleLambda  ▪  MangoldtLambda  ▪  Mod  ▪  PowerMod  ▪  ...

Perfect Numbers

PerfectNumber th perfect number

PerfectNumberQ  ▪  MersennePrimeExponent  ▪  MersennePrimeExponentQ


DivisorSum compute a sum over divisors

DirichletConvolve Dirichlet convolution of sequences

Sum  ▪  Product  ▪  Integrate  ▪  Series  ▪  Limit