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
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