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
Operations
DivisorSum — compute a sum over divisors
DirichletConvolve — Dirichlet convolution of sequences