# Number of divisors function

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In number theory the **number of divisors function** of a positive integer, denoted *d*(*n*) or τ(*n*) or σ_{0}(*n*), is the number of positive integer divisors of the number *n*.

It is a multiplicative function, that is *m* and *n* are coprime then .

The value of *d* on a general integer *n* with prime factorisation

is then

The average order of *d*(*n*) is .
The normal order of log(*d*(*n*)) is log(2) log log(*n*).