FiniteAbelianGroupCount
FiniteAbelianGroupCount[n] gives the number of finite Abelian groups of order n.
Examples
Count finite Abelian groups of order 12:
FiniteAbelianGroupCount[12]Count for a range of orders:
Table[FiniteAbelianGroupCount[n], {n, 1, 20}]Please visit the official Wolfram Language Reference for more details.