In mathematics, a natural number a is a unitary divisor of a number b if a and 
are coprime, having no common factor other than 1. Thus, 5 is a unitary divisor of 60, because 5 and 
have only 1 as a common factor, while 6 is a divisor but not a unitary divisor of 60, as 6 and 
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). (sequence A034448 in OEIS) gives the value of this function for the first few positive integers, while A034444 gives the count of unitary divisors.
The number of unitary divisors of a number n is 2k, where k is the number of prime factors of n.
References
- Richard K. Guy (2004). Unsolved Problems in Number Theory. Springer-Verlag. p. 84. ISBN 0-387-20860-7. Section B3.
- Paulo Ribenboim (2000). My Numbers, My Friends: Popular Lectures on Number Theory. Springer-Verlag. p. 352. ISBN 0-387-98911-0.
External links
- Weisstein, Eric W., "Unitary Divisor" from MathWorld.
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