The first two perfect numbers are 6 and 28
A number is perfect if it is equal to the sum of its factors other than itself: e.g. 6 = 1 + 2 + 3 and 28 = 1+ 2 + 4 + 7 + 14.
The first four triangular numbers are 1, 3, 6, 10. Both 6 and 28 are triangular numbers. Are all perfect numbers triangular?
The first four hexagonal numbers are 1, 6, 15, 28. Both 6 and 28 are hexagonal numbers. Are all perfect numbers hexagonal?
(reproduced with permission from Mathematics in Education and Industry)
