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.
IntegerPartitions — find restricted and unrestricted partitions of integers
PartitionsP ▪ PartitionsQ
IntegerDigits ▪ MixedRadix ▪ NumberDecompose
Representation in Terms of Powers
PowersRepresentations — find representations of integers as sums of powers
SquaresR ▪ FrobeniusNumber ▪ FrobeniusSolve ▪ Reduce ▪ Solve
Sum, Product — general symbolic sums and products
DirichletConvolve ▪ DivisorSum ▪ DiscreteConvolve
PrimeOmega, PrimeNu — number of distinct prime factors (with, without multiplicities)
Mod ▪ EulerPhi ▪ MoebiusMu ▪ DivisorSigma ▪ ...