Is 11 a deficient number?
Primes, prime powers, and any divisors of a perfect or deficient number are all deficient. The first few deficient numbers are 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, (OEIS A005100).
Is 11 abundant deficient or perfect?
Deficient numbers occur more frequently than abundant numbers. In other words, the sum of the proper divisors of most numbers is less than the numbers themselves. Examples of deficient numbers include 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, and 23.
How do you know a number is deficient?
A number n is said to be Deficient Number if sum of all the divisors of the number denoted by divisorsSum(n) is less than twice the value of the number n. And the difference between these two values is called the deficiency.
What does deficient mean in math?
deficient number. • a number that is larger than the sum of its proper divisors.
What makes a number deficient?
In number theory, a deficient number or defective number is a number n for which the sum of divisors of n is less than 2n. For example, the proper divisors of 8 are 1, 2, and 4, and their sum is less than 8, so 8 is deficient.
Why is 1 a deficient number?
In order for a number to be a deficient number, the sum of the proper factors of the number must be smaller than the number, not greater, or equal to the number. The first 20 deficient numbers are 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, and 25.
Is 11 an abundant number?
The first 28 abundant numbers are: 12, 18, 20, 24, 30, 36, 40, 42, 48, 54, 56, 60, 66, 70, 72, 78, 80, 84, 88, 90, 96, 100, 102, 104, 108, 112, 114, 120, (sequence A005101 in the OEIS). Because 36 is greater than 24, the number 24 is abundant.
What are abundant and deficient numbers?
Abundant: The sum of the proper factors is greater than the number itself. Deficient: The sum of the proper factors is less than the number itself. Perfect: The sum of the proper factors is equal to than the number itself. 1.
When is a number called a deficient number?
A number n is said to be Deficient Number if sum of all the divisors of the number denoted by divisorsSum (n) is less than twice the value of the number n. And the difference between these two values is called the deficiency. 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19 …..
Are there any odd numbers that are deficient?
More generally, all odd numbers with one or two distinct prime factors are deficient. It follows that there are infinitely many odd deficient numbers. There are also an infinite number even deficient numbers as all powers of two are ( 1 + 2 + 4 + 8 + + 2x-1 = 2x – 1 ). .
Is the number 21 a deficient prime number?
Its proper divisors are 1, 3 and 7, and their sum is 11. Because 11 is less than 21, the number 21 is deficient. Its deficiency is 2 × 21 − 32 = 10. Since the aliquot sums of prime numbers equal 1, all prime numbers are deficient.
Which is an abundant number and which is deficient?
Because the sum of its proper divisors (1 + 2 + 3 + 4 + 6 = 16) is greater than 12, 12 is an abundant number. Numbers like 8, whose proper divisors have a sum that is less than the number itself, are called deficient or defective.