Perfect Number Calculator
Check if numbers are perfect, abundant, or deficient. Find amicable pairs and explore aliquot sequences.
Input
Proper Divisors of 28:
1, 2, 4, 7, 14
Sum: 1 + 2 + 4 + 7 + 14 = 28
Definitions:
- Perfect: Sum of divisors = n
- Abundant: Sum of divisors > n
- Deficient: Sum of divisors < n
28 is
PERFECT
Sum of divisors equals the number!
Aliquot Sequence
2828
Known Perfect Numbers
6
28
496
8,128
Amicable Pairs Found
(220, 284)
(1184, 1210)
(2620, 2924)
(5020, 5564)
(6232, 6368)
Perfect Numbers and Mersenne Primes
Even perfect numbers are given by the formula: 2^(p-1) × (2^p - 1) where (2^p - 1) is a Mersenne prime.
| p | Mersenne (2^p - 1) | Perfect Number |
|---|---|---|
| 2 | 3 | 6 |
| 3 | 7 | 28 |
| 5 | 31 | 496 |
| 7 | 127 | 8,128 |
| 13 | 8,191 | 33,550,336 |
| 17 | 131,071 | 8,589,869,056 |