Perfect number - Wikipedia, the free encyclopedia
In mathematics, a perfect number is defined as a positive integer which is the sum of its proper positive divisors, that is, the sum of the positive divisors excluding the number itself. Equivalentl...
en.wikipedia.org/wiki/Perfect_number
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It is not known when perfect numbers were first studied and indeed the first studies may go back to the earliest times when numbers first aroused curiosity. ... 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.
www.gap-system.org/~history/HistTopics/Perfect_numbers.... www.gap-system.org/~history/HistTopics/Perfect_numbers.html
Lemma 1: In a magic square of order four, the sum of the corners is K. ... If S = the sum of all integers which exactly divide N, including 1 and N, then "perfect numbers" are S = 2 N; the first three numbers which are S = 3 N are: ... The first four perfect numbers are 6, 28, 496, 8128.
www.inwap.com/pdp10/hbaker/hakmem/number.html www.inwap.com/pdp10/hbaker/hakmem/number.html
You may have also noticed that the perfect numbers listed above (6, 28, 496, 8128) all end with either the digit 6 or the digit 8--this is also very easy to prove (but no, they do not continue to alternate 6, 8, 6, 8,...). If you like that digit pattern, look at the first four perfect numbers in binary:
primes.utm.edu/mersenne/
One example is the perfect numbers, those integers which are the sum of their positive proper divisors. The first three perfect numbers are...
primes.utm.edu/glossary/page.php?sort=PerfectNumber primes.utm.edu/glossary/page.php?sort=PerfectNumber
C Programming question: Make a program that displays the first four perfect numbers? int main (void) { puts (6 28 496 8128); return 0; } ... What are the first four perfect numbers using program? Write a program that displays the first four perfect numbers? How do you make a program that displays the first four...
wiki.answers.com/Q/Make_a_program_that_displays_the_fir... wiki.answers.com/Q/Make_a_program_that_displays_the_first_four_perfect_numbers
The first four perfect numbers, which are the sum of their natural divisors. Although the first is unique in a variety of ways, the rest of the progression follows other interesting rules. Each is, for example, the sum of the cubes of consecutive odd numbers.
www.organelle.org/organelle/tetra/tetraB.html
There are far more defective and abundant numbers than perfect numbers. However, do abundant numbers actually outnumber defective numbers? I'm not sure. ... Here are the first four perfect numbers: 110, 11100, 111110000, 1111111000000. See a pattern?
www.maa.org/mathland/mathtrek_5_18_98.html
For example, the final digits of the four perfect numbers that he knew alternate between 6 and 8. It turns out that the final digit of an even perfect number is always 6 or 8, ... The first four perfect numbers written in binary form also display a striking pattern: 110, 11100, 11111000, and 11111110000!
www.maa.org/mathland/mathtrek_01_20_03.html
The first four perfect numbers were known over 2,000 years ago. Some ancient cultures gave mystic interpretations to numbers that they thought were magic. ... So, our first five perfect numbers are ... The first 35 perfect numbers fit this same formula with "n" values of:
mathforum.org/dr.math/faq/faq.perfect.html mathforum.org/dr.math/faq/faq.perfect.html
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