perfect numbers

### Author Topic: perfect numbers  (Read 903 times)

#### jas_fluidm

• Faculty
• Sr. Member
• Posts: 291
##### perfect numbers
« 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

#### arefin

• Hero Member
• Posts: 1173
• Associate Professor, Dept. of ETE, FE
##### Re: perfect numbers
« Reply #1 on: March 04, 2012, 06:24:32 PM »
Thanks for sharing.
“Allahumma inni as'aluka 'Ilman naafi'an, wa rizqan tayyiban, wa 'amalan mutaqabbalan”

O Allah! I ask You for knowledge that is of benefit, a good provision and deeds that will be accepted. [Ibne Majah & Others]
.............................
Taslim Arefin
Assistant Professor
Dept. of ETE, FE
DIU

#### jas_fluidm

• Faculty
• Sr. Member
• Posts: 291
##### Re: perfect numbers
« Reply #2 on: March 05, 2012, 03:00:22 PM »
thanks for the complement

#### Masuma Parvin

• Sr. Member
• Posts: 323
##### Re: perfect numbers
« Reply #3 on: March 06, 2012, 04:49:30 PM »
Very interesting.Thanks for the post.

#### tasnuva

• Sr. Member
• Posts: 344
##### Re: perfect numbers
« Reply #4 on: March 07, 2012, 05:45:49 PM »
Nice post.
Tasnuva Ali
Senior Lecturer
Department of ETE
Daffodil International university

#### Sima

• Full Member
• Posts: 176
##### Re: perfect numbers
« Reply #5 on: March 13, 2012, 02:29:51 PM »
Good to know the history...
Sima Rani Dey
Lecturer
Dept. of Natural Sciences