Definition:Perfect Number/Sequence
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Sequence of Perfect Numbers
The sequence of perfect numbers begins:
| \(\ds 6\) | \(=\) | \(\ds 2^{2 - 1} \times \paren {2^2 - 1}\) | ||||||||||||
| \(\ds 28\) | \(=\) | \(\ds 2^{3 - 1} \times \paren {2^3 - 1}\) | ||||||||||||
| \(\ds 496\) | \(=\) | \(\ds 2^{5 - 1} \times \paren {2^5 - 1}\) | ||||||||||||
| \(\ds 8128\) | \(=\) | \(\ds 2^{7 - 1} \times \paren {2^7 - 1}\) | ||||||||||||
| \(\ds 33 \, 550 \, 336\) | \(=\) | \(\ds 2^{13 - 1} \times \paren {2^{13} - 1}\) | ||||||||||||
| \(\ds 8 \, 589 \, 869 \, 056\) | \(=\) | \(\ds 2^{17 - 1} \times \paren {2^{17} - 1}\) |
This sequence is A000396 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
Sources
- 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