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BUILT-IN MATHEMATICA SYMBOL

FiniteAbelianGroupCount

FiniteAbelianGroupCount[n]
gives the number of finite Abelian groups of order n.

Integer mathematical function, suitable for both symbolic and numerical manipulation.

Table of values:

Out[1]=

Out[1]=

Evaluate for large arguments:

FiniteAbelianGroupCount threads element-wise over lists:

Number of non-Abelian groups of order n:

Compare cumulative counts of even and odd numbers of Abelian groups:

The number of finite Abelian groups can be found using PartitionsP:

FiniteAbelianGroupCount[n] depends only on prime exponents of n:

FiniteAbelianGroupCount is a multiplicative function:

FiniteAbelianGroupCount evaluates only for explicit integer values:

Use Simplify to find implicit integers in arguments:

Successive differences of FiniteAbelianGroupCount modulo 2: