Perfect Number/Sequence

Sequence of Perfect Numbers

The sequence of perfect numbers begins:

$\ds 6$

$=$

$\ds 2^{2 - 1} \times \paren {2^2 - 1}$

$\ds 28$

$=$

$\ds 2^{3 - 1} \times \paren {2^3 - 1}$

$\ds 496$

$=$

$\ds 2^{5 - 1} \times \paren {2^5 - 1}$

$\ds 8128$

$=$

$\ds 2^{7 - 1} \times \paren {2^7 - 1}$

$\ds 33 \, 550 \, 336$

$=$

$\ds 2^{13 - 1} \times \paren {2^{13} - 1}$

$\ds 8 \, 589 \, 869 \, 056$

$=$

$\ds 2^{17 - 1} \times \paren {2^{17} - 1}$

1971: George E. Andrews: Number Theory ... (previous) ... (next): $\text {3-5}$ The Use of Computers in Number Theory
1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {B}.2$: More about Numbers: Irrationals, Perfect Numbers and Mersenne Primes
1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): perfect number
2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): perfect number