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numlib::tau

Number of divisors of an integer

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Syntax

numlib::tau(n)

Description

numlib::tau(n) returns the number of positive divisors of n.

numlib::tau(0) returns 0.

numlib::tau returns the function call with evaluated argument if the argument is not a number.

numlib::tau returns an error if the argument evaluates to a number of wrong type.

numlib::tau is the same function as numlib::numdivisors.

Examples

Example 1

We compute the number of positive divisors of the number 6746328388800 (one of the highly composite numbers studied by S. Ramanujan in 1915):

numlib::tau(6746328388800)

Parameters

n

An integer

Return Values

numlib::tau returns a nonnegative integer.

Algorithms

Internally, ifactor is used for factoring n.

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