Semiperfect Number Calculator

Welcome to use the Semiperfect Number Calculator, which can help you quickly verify whether the number is a semiperfect number.

A semiperfect number, also known as a pseudoperfect number, means that the sum of all or some of proper factors of a positive integer is exactly equal to itself, then the positive integer is called a semi-perfect number.

Obviously, all perfect numbers are semiperfect numbers, because the sum of all proper factors of a perfect number is exactly equal to itself. The deficient number can’t be a semiperfect number, because the sum of all proper factors of a deficient number is less than itself.

For example: Is 20 a semiperfect number?

The factors of 20 are 1, 2, 4, 5, 10 and 20. The proper factors of 20 are 1, 2, 4, 5, 10. Among them, 1 + 4 + 5 + 10 =20. So, 20 is a semiperfect number.

Another example: the proper factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, and 24.

8 + 16 + 24 = 48.

1 + 3 + 4 + 16 + 24 = 48.

1 + 2 + 3 + 6 + 8 + 12 + 16 = 48.

and so on.

So, 48 is a semi-perfect number.

The semiperfect numbers within 100 are:

• 6
• 12
• 18
• 20
• 24
• 28
• 30
• 36
• 40
• 42
• 48
• 54
• 56
• 60
• 66
• 72
• 78
• 80
• 84
• 88
• 90
• 96
• 100

The procedure to use the semiperfect number calculator is as follows: