Building on its broad algorithmic and mathematical capabilities, the Wolfram Language provides a unique level of highly general and efficient support for additive number theory.

Integer Partitions

IntegerPartitions — find restricted and unrestricted partitions of integers

PartitionsP  ▪  PartitionsQ

Base-Like Representations

IntegerDigits  ▪  MixedRadix  ▪  NumberDecompose

Representation in Terms of Powers

PowersRepresentations — find representations of integers as sums of powers

SquaresR  ▪  FrobeniusNumber  ▪  FrobeniusSolve  ▪  Reduce  ▪  Solve

Summation-Related Operations

Sum, Product — general symbolic sums and products

DirichletConvolve  ▪  DivisorSum  ▪  DigitSum  ▪  DiscreteConvolve

Arithmetic Functions »

PrimeOmega, PrimeNu — number of distinct prime factors (with, without multiplicities)

Mod  ▪  EulerPhi  ▪  MoebiusMu  ▪  DivisorSigma  ▪  ...