perfect numbers

[jas_fluidm]

In number theory, a perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself (also known as its aliquot sum). Equivalently, a perfect number is a number that is half the sum of all of its positive divisors (including itself) i.e. σ1(n) = 2n.
The list of the perfect numbers are as follows:
6
28
496
8128
33550336
8589869056
137438691328
.......................


The four perfect numbers 6, 28, 496 and 8128 seem to have been known from ancient times and there is no record of these discoveries.

    6 = 1 + 2 + 3,
    28 = 1 + 2 + 4 + 7 + 14,
    496 = 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248
    8128 = 1 + 2 + 4 + 8 + 16 + 32 + 64 + 127 + 254 + 508 + 1016 + 2032 + 4064

[arefin]

Thanks for sharing.

[jas_fluidm]

thanks for the complement

[Masuma Parvin]

Very interesting.Thanks for the post.

[tasnuva]

Nice post.

[Sima]

Good to know the history...