Daffodil International University

Science & Information Technology => Science Discussion Forum => Topic started by: jas_fluidm on March 04, 2012, 04:08:36 PM

Title: perfect numbers
Post by: jas_fluidm on March 04, 2012, 04:08:36 PM

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

Title: Re: perfect numbers
Post by: arefin on March 04, 2012, 06:24:32 PM

Thanks for sharing.

Title: Re: perfect numbers
Post by: jas_fluidm on March 05, 2012, 03:00:22 PM

thanks for the complement

Title: Re: perfect numbers
Post by: Masuma Parvin on March 06, 2012, 04:49:30 PM

Very interesting.Thanks for the post.

Title: Re: perfect numbers
Post by: tasnuva on March 07, 2012, 05:45:49 PM

Nice post.

Title: Re: perfect numbers
Post by: Sima on March 13, 2012, 02:29:51 PM

Good to know the history...