Editing Practical number (section)

==Properties==
*The only odd practical number is 1, because if <math>n</math> is an odd number greater than 2, then 2 cannot be expressed as the sum of distinct divisors {{nowrap|of <math>n</math>.}} More strongly, {{harvtxt|Srinivasan|1948}} observes that other than 1 and 2, every practical number is divisible by 4 or 6 (or both).
*The product of two practical numbers is also a practical number.{{sfnp|Margenstern|1991}} Equivalently, the set of all practical numbers is closed under multiplication. More strongly, the [[least common multiple]] of any two practical numbers is also a practical number. 
*From the above characterization by Stewart and Sierpiński it can be seen that if <math>n</math> is a practical number and <math>d</math> is one of its divisors then <math>n\cdot d</math> must also be a practical number. Furthermore, a practical number multiplied by power combinations of any of its divisors is also practical.
*In the set of all practical numbers there is a primitive set of practical numbers. A primitive practical number is either practical and [[squarefree]] or practical and when divided by any of its prime factors whose [[Prime factorization|factorization]] exponent is greater than 1 is no longer practical. The sequence of primitive practical numbers {{OEIS|A267124|}} begins
{{bi|left=3.2|1, 2, 6, 20, 28, 30, 42, 66, 78, 88, 104, 140, 204, 210, 220, 228, 260, 272, 276, 304, 306, 308, 330, 340, 342, 348, 364, 368, 380, 390, 414, 460 ...}}
*Every positive integer has a practical multiple. For instance, for every integer <math>n</math>, its multiple <math>2^{\lfloor\log_2 n\rfloor}n</math> is practical.{{sfnp|Eppstein|2021}}
*Every odd prime has a primitive practical multiple. For instance, for every odd prime <math>p</math>, its multiple <math>2^{\lfloor\log_2 p\rfloor}p</math> is primitive practical. This is because <math>2^{\lfloor\log_2 p\rfloor}p</math> is practical{{sfnp|Eppstein|2021}} but when divided by 2 is no longer practical. A good example is a [[Mersenne prime]] of the form <math>2^p-1</math>. Its primitive practical multiple is <math>2^{p-1}(2^p-1)</math> which is an even [[perfect number]].