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:
“It might be seen by what tenure men held the earth. The smallest stream is mediterranean sea, a smaller ocean creek within the land, where men may steer by their farm bounds and cottage lights. For my own part, but for the geographers, I should hardly have known how large a portion of our globe is water, my life has chiefly passed within so deep a cove. Yet I have sometimes ventured as far as to the mouth of my Snug Harbor.”
—Henry David Thoreau (1817–1862)
“... there are persons who seem to have overcome obstacles and by character and perseverance to have risen to the top. But we have no record of the numbers of able persons who fall by the wayside, persons who, with enough encouragement and opportunity, might make great contributions.”
—Mary Barnett Gilson (1877–?)