Smallest k-perfect Numbers
The following table gives an overview of the smallest k-perfect numbers for k <= 7 (sequence A007539 in OEIS):
| k | Smallest k-perfect number | Found by |
|---|---|---|
| 1 | 1 | ancient |
| 2 | 6 | ancient |
| 3 | 120 | ancient |
| 4 | 30240 | René Descartes, circa 1638 |
| 5 | 14182439040 | René Descartes, circa 1638 |
| 6 | 154345556085770649600 | Robert Daniel Carmichael, 1907 |
| 7 | 141310897947438348259849402738 485523264343544818565120000 | TE Mason, 1911 |
For example, 120 is 3-perfect because the sum of the divisors of 120 is
1+2+3+4+5+6+8+10+12+15+20+24+30+40+60+120 = 360 = 3 × 120.
Read more about this topic: Multiply Perfect Number
Famous quotes containing the words smallest and/or numbers:
“The smallest flower is a thought, a life answering to some feature of the Great Whole, of whom they have a persistent intuition.”
—Honoré De Balzac (1799–1850)
“Our religion vulgarly stands on numbers of believers. Whenever the appeal is made—no matter how indirectly—to numbers, proclamation is then and there made, that religion is not. He that finds God a sweet, enveloping presence, who shall dare to come in?”
—Ralph Waldo Emerson (1803–1882)