Editing Practical number (section)

==Relation to other classes of numbers==
Several other notable sets of integers consist only of practical numbers:
*From the above properties with <math>n</math> a practical number and <math>d</math> one of its divisors (that is, <math>d|n</math>) then <math>n\cdot d</math> must also be a practical number therefore six times every power of 3 must be a practical number as well as six times every power of 2.
*Every [[power of two]] is a practical number.<ref name="s48"/> Powers of two trivially satisfy the characterization of practical numbers in terms of their prime factorizations: the only prime in their factorizations, ''p''<sub>1</sub>, equals two as required. 
*Every even [[perfect number]] is also a practical number.<ref name="s48"/> This follows from [[Leonhard Euler]]'s result that an even perfect number must have the form <math>2^{k-1}(2^k-1)</math>. The odd part of this factorization equals the sum of the divisors of the even part, so every odd prime factor of such a number must be at most the sum of the divisors of the even part of the number. Therefore, this number must satisfy the characterization of practical numbers. A similar argument can be used to show that an even perfect number when divided by 2 is no longer practical. Therefore, every even perfect number is also a primitive practical number.
*Every [[primorial]] (the product of the first <math>i</math> primes, for some <math>i</math>) is practical.<ref name="s48"/> For the first two primorials, two and six, this is clear. Each successive primorial is formed by multiplying a prime number <math>p_i</math> by a smaller primorial that is divisible by both two and the next smaller prime, <math>p_{i-1}</math>. By [[Bertrand's postulate]], <math>p_i<2p_{i-1}</math>, so each successive prime factor in the primorial is less than one of the divisors of the previous primorial. By induction, it follows that every primorial satisfies the characterization of practical numbers. Because a primorial is, by definition, squarefree it is also a primitive practical number.
*Generalizing the primorials, any number that is the product of nonzero powers of the first <math>k</math> primes must also be practical. This includes [[Ramanujan]]'s [[highly composite number]]s (numbers with more divisors than any smaller positive integer) as well as the [[factorial]] numbers.<ref name="s48">{{harvtxt|Srinivasan|1948}}.</ref>