what is a practical number? can anyone give me an example?

Question

thanks!

one of the answers says that the divisors of 12 are: 1, 2, 3, and 6

why is 4 not included??

Answer 1

A practical number or panarithmic number is a positive integer n such that all smaller positive integers can be represented as sums of distinct divisors of n. For example, 12 is a practical number because all the numbers from 1 to 11 can be expressed as sums of its divisors 1, 2, 3, and 6: as well as these divisors themselves, we have 4=3+1, 5=3+2, 7=6+1, 8=6+2, 9=6+3, 10=6+3+1, and 11=6+3+2. Any even perfect number and any power of two is also a practical number.

Answer 2

practical number or panarithmic number is a positive integer n such that all smaller positive integers can be represented as sums of distinct divisors of n. For example, 12 is a practical number because all the numbers from 1 to 11 can be expressed as sums of its divisors 1, 2, 3, and 6: as well as these divisors themselves, we have 4=3+1, 5=3+2, 7=6+1, 8=6+2, 9=6+3, 10=6+3+1, and 11=6+3+2. Any even perfect number and any power of two is also a practical number.

Answer 3

A practical number or panarithmic number is a positive integer n such that all smaller positive integers can be represented as sums of distinct divisors of n. For example, 12 is a practical number because all the numbers from 1 to 11 can be expressed as sums of its divisors 1, 2, 3, and 6: as well as these divisors themselves, we have 4=3+1, 5=3+2, 7=6+1, 8=6+2, 9=6+3, 10=6+3+1, and 11=6+3+2. Any even perfect number and any power of two is also a practical number.