Multiply Perfect Number - Smallest k-perfect Numbers

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.

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