Perfect Number


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perfect number

[′pər·fikt ′nəm·bər]
(mathematics)
An integer which equals the sum of all its factors other than itself.

Perfect Number

 

a positive integer that is equal to the sum of all its factors except itself. Examples of perfect numbers are 6 = 1 + 2 + 3 and 28 = 1 + 2 + 4 + 7 + 14.

As early as the third century B.C., Euclid showed that even perfect numbers could be obtained from the formula 2p–l(2p – 1) when p and 2p – 1 are prime numbers. Approximately 20 even perfect numbers have been found in this way. As of 1976, no odd perfect numbers are known, and their existence remains an open question. Perfect numbers were first investigated by the Pythagoreans, who ascribed a special mystical meaning to such numbers and combinations of such numbers.

perfect number

equal in value to the sum of those natural numbers that are less than the given number but that also divide (with zero remainder) the given number. [Math.: EB, VII: 872]
References in periodicals archive ?
14) To explain: in number theory, a perfect number is a positive integer that is equal to the sum of its proper positive divisors (i.
Potential fantasy MVP Chris Davis is also involved in all these second-half look-aheads, as his first-half homer total of 37 puts him on pace for 62 blasts, the perfect number to spark debate.
Today's report is perhaps the perfect number for nervous investors," said James Marple, Senior Economist at TD Economics.
It is an indicator; it's not a perfect number," he said.
Over several years of experimentation, feedback and a certain fondness for an old Three Dog Night song (or another similarly titled by U2), I have now arrived at the perfect number of resolutions to share that may stand some small chance of surviving past the end of this article.
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23pm that the group of girls (4 polled as the perfect number for a night out) are ready to leave, uploading an average of eight photos to Facebook and Twitter throughout the evening.
Six is a perfect number, so that may affect your results.
The truth is there is no hard and fast rule or a single formula to find the perfect number because every person has different retirement goals, income level and lifestyle.
The numbers themselves are interesting: 6 is a perfect number (its proper factors have a sum of 6); 9 is a square number (3^2 = 9); and 12 is the least abundant number (its proper factors have a sum greater than 12).
What many teachers, administrators and parents would like to know is the magic number for each grade level--the perfect number of students to have in a classroom.
It is labeled the Perfect Number as all other figures start and end with it and repeat themselves after it.