Building on its broad algorithmic and mathematical capabilities,
Mathematica provides a unique level of highly general and efficient support for additive number theory.
IntegerPartitions — find restricted and unrestricted partitions of integers
PowersRepresentations — find representations of integers as sums of powers
Sum,
Product — general symbolic sums and products
PrimeOmega,
PrimeNu — number of distinct prime factors (with, without multiplicities)
