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   ▪ ...