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

Operations

DivisorSum — compute a sum over divisors

DirichletConvolve — Dirichlet convolution of sequences

Sum   ▪ Product   ▪ Integrate   ▪ Series   ▪ Limit

Related Guides

▪
• Additive Number Theory
▪
• Analytic Number Theory
▪
• General Number Theory