Types of Composite Numbers
One way to classify composite numbers is by counting the number of prime factors. A composite number with two prime factors is a semiprime or 2-almost prime (the factors need not be distinct, hence squares of primes are included). A composite number with three distinct prime factors is a sphenic number. In some applications, it is necessary to differentiate between composite numbers with an odd number of distinct prime factors and those with an even number of distinct prime factors. For the latter
(where μ is the Möbius function and x is half the total of prime factors), while for the former
Note however that for prime numbers the function also returns -1, and that . For a number n with one or more repeated prime factors, .
If all the prime factors of a number are repeated it is called a powerful number. If none of its prime factors are repeated, it is called squarefree. (All prime numbers and 1 are squarefree.)
Another way to classify composite numbers is by counting the number of divisors. All composite numbers have at least three divisors. In the case of squares of primes, those divisors are . A number n that has more divisors than any x < n is a highly composite number (though the first two such numbers are 1 and 2).
Read more about this topic: Composite Number
Famous quotes containing the words types of, types, composite and/or numbers:
“Our children evaluate themselves based on the opinions we have of them. When we use harsh words, biting comments, and a sarcastic tone of voice, we plant the seeds of self-doubt in their developing minds.... Children who receive a steady diet of these types of messages end up feeling powerless, inadequate, and unimportant. They start to believe that they are bad, and that they can never do enough.”
—Stephanie Martson (20th century)
“The rank and file have let their servants become their masters and dictators.... Provision should be made in all union constitutions for the recall of leaders. Big salaries should not be paid. Career hunters should be driven out, as well as leaders who use labor for political ends. These types are menaces to the advancement of labor.”
—Mother Jones (1830–1930)
“A positive learning climate in a school for young children is a composite of many things. It is an attitude that respects children. It is a place where children receive guidance and encouragement from the responsible adults around them. It is an environment where children can experiment and try out new ideas without fear of failure. It is an atmosphere that builds children’s self-confidence so they dare to take risks. It is an environment that nurtures a love of learning.”
—Carol B. Hillman (20th century)
“I had a feeling that out there, there were very poor people who didn’t have enough to eat. But they wore wonderfully colored rags and did musical numbers up and down the streets together.”
—Jill Robinson (b. 1936)