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PrimeNu

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

PrimeNu[n] gives the number of distinct prime factors of n, nu(n). PrimeNu[n, GaussianIntegers -> True] (or a non-real Gaussian-integer n) counts distinct Gaussian prime factors over Z[i]. PrimeNu[1] is 0; PrimeNu[0] is left unevaluated.

Examples

All examples below are verified against the current Mathilda build.

In[1]:= PrimeNu[24]
Out[1]= 2

In[2]:= PrimeNu[105]
Out[2]= 3

In[3]:= PrimeNu[{4, 28, 180}]
Out[3]= {1, 2, 3}

In[4]:= PrimeNu[50!]
Out[4]= 15

In[5]:= PrimeNu[3 + I]
Out[5]= 2

In[6]:= PrimeNu[105, GaussianIntegers -> True]
Out[6]= 4

Implementation notes

  • Listable, Protected.
  • Additive on coprime arguments: nu(m n) = nu(m) + nu(n) when

Attributes: Listable, Protected.

Implementation status

Stable — documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

References