# Definition:Perfect Number/Definition 1

## Definition

A perfect number is a (strictly) positive integer equal to its aliquot sum.

## Sequence of Perfect Numbers

The sequence of perfect numbers begins:

 $\ds 6$ $=$ $\ds 2^{2 - 1} \times \paren {2^2 - 1}$ $\ds 28$ $=$ $\ds 2^{3 - 1} \times \paren {2^3 - 1}$ $\ds 496$ $=$ $\ds 2^{5 - 1} \times \paren {2^5 - 1}$ $\ds 8128$ $=$ $\ds 2^{7 - 1} \times \paren {2^7 - 1}$ $\ds 33 \, 550 \, 336$ $=$ $\ds 2^{13 - 1} \times \paren {2^{13} - 1}$ $\ds 8 \, 589 \, 869 \, 056$ $=$ $\ds 2^{17 - 1} \times \paren {2^{17} - 1}$