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PartitionsP

PartitionsP[n]
gives the number

of unrestricted partitions of the integer n.

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

Plot the number of unrestricted partitions:

Out[1]=

Plot the number of unrestricted partitions:

Out[1]=

Compute the number of partitions for large numbers:

PartitionsP threads element-wise over lists:

Number of non-isomorphic Abelian groups of order

Compare cumulative counts of even and odd partitions:

Visualize p-adic valuations of the number of partitions:

Obtain values of PartitionsP from series expansion:

Use FullSimplify to simplify expressions containing PartitionsP:

PartitionsP evaluates only for integer arguments:

Use Simplify to find implicit integers in arguments:

Successive differences of PartitionsP modulo 2:

A "random" walk based on PartitionsP: