Perfect Number is Sum of Successive Odd Cubes except 6/Mistake
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Source Work
1986: David Wells: Curious and Interesting Numbers:
- The Dictionary
- $6$
1997: David Wells: Curious and Interesting Numbers (2nd ed.):
- The Dictionary
- $6$
Mistake
- [ $6$ ] is the only perfect number that is not the sum of successive cubes.
Correction
The statement should be:
- [ $6$ ] is the only even perfect number that is not the sum of successive odd cubes.
For example:
- $496 = 1 + 27 + 125 + 343 = 1^3 + 3^3 + 5^3 + 7^3$
It is appreciated that it is not known whether there exist any odd perfect numbers.
However, for complete accuracy it is necessary to include a qualification of the parity of the perfect numbers for which the statement does in fact hold.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $6$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $6$