Unitary divisor

In mathematics, a natural number $a$ is a unitary divisor of a number $b$ if $a$ and $frac\{b\}\{a\}$ are coprime, having no common factor other than 1. Thus, 5 is a unitary divisor of 60, because 5 and $frac\{60\}\{5\}=12$ have only 1 as a common factor, while 6 is a divisor but not a unitary divisor of 60, as 6 and $frac\{60\}\{6\}=10$ have a common factor other than 1, namely 2. 1 is a unitary divisor of every natural number.

If the proper unitary divisors of a given number add up to that number, then that number is a unitary perfect number. The sum of unitary divisors function is denoted by the lowercase Greek letter sigma thus: σ*("n"). OEIS|id=A034448 gives the value of this function for the first few positive integers, while OEIS2C|id=A034444 gives the count of unitary divisors.

The number of unitary divisors of a number "n" is 2^"k", where "k" is the number of prime factors of "n".

References

* Section B3.
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External links

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