We knew numbers could be odd.. but who knew numbers can be deficient, weird, amicable, friendly, sociable, solitary, sublime, frugal, and extravagant.
But we all knew it is easier to be semi- or pseudo-perfect than to be perfect though you could aim to be hyper-perfect! However, it is very difficult to be sublime! (There are only two known sublime numbers, 12 and 6086555670238378989670371734243169622657830773351885970528324860512791691264.)
Being friendly or better still an amicable pair seems like fun though. And if you are weird, you are abundant but not semiperfect.
So kids, learn your math! Numbers and mathematics can teach us so much about people and life. :)
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* You can stop reading now if you are not interested in geeky mathematic details. From wikipedia, I am transcribing here some of interesting information about perfect numbers and their relation to prime numbers - specifically Mersenne primes.
A semiperfect or pseudoperfect number is a number that is equal to the sum of all or some of its proper divisors. The first few semiperfect numbers are 6, 12, 18, 20, 24, 28, 30, 36, 40, .. (not all even ... but the smallest odd semiperfect number is 945.)
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 not including the number itself. The first perfect number is 6, because 1, 2, and 3 are its proper positive divisors and 1 + 2 + 3 = 6. The next perfect number is 28 = 1 + 2 + 4 + 7 + 14. The next perfect numbers are 496 and 8128.
Greek mathematicians knew only these four perfect numbers. Euclid discovered that the first four perfect numbers are generated by the formula 2n−1(2n − 1), where n = 2, 3, 5, 7. Noticing that 2n − 1 is a prime number in each instance, Euclid proved that the formula 2n−1(2n − 1) gives an even perfect number whenever 2n − 1 is prime. In order for 2n − 1 to be prime, it is necessary but not sufficient that n should be prime.
The Arabic mathematician Ibn al-Haytham had conjectured (around 1000 AD) that every even perfect number is of the form 2n−1(2n − 1) where 2n − 1 is prime but it was not until the 18th century that Leonhard Euler proved that the formula 2n−1(2n − 1) will yield all the even perfect numbers.
Prime numbers of the form 2n − 1 are known as Mersenne primes, after the seventeenth-century monk Marin Mersenne, who studied number theory and perfect numbers. As of September 2007, only 44 Mersenne primes are known, which means there are 44 perfect numbers known, the largest being 232,582,656 × (232,582,657 − 1) with 19,616,714 digits.
And speaking of prime numbers, of which the Mersennes are just a small subset:
The prime number theorem describes the asymptotic distribution of the prime numbers. It states that if you randomly select a number nearby some large number N, the chance of it being prime is about 1 / ln(N), where ln(N) denotes the natural logarithm of N.
The prime counting function is the function pi(x) giving the number of primes less than or equal to a given number x.
The growth rate of the prime-counting function was conjectured in the late 18th century by Gauss and by Legendre and first proved independently by Jacques Hadamard and Charles de la Vallée Poussin in 1896, using properties of the Riemann zeta function introduced by Bernhard Riemann in 1859. Elementary proofs of the prime number theorem not using the zeta function or complex analysis were found around 1948 by Atle Selberg and by Paul Erdős .
If you are learning more about prime numbers, a very fascinating subject, read Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics by John Derbyshire and peruse through the treasure-chest of information at Prof. Chris Caldwell's Prime Pages.
For more about Riemann's hypothesis, read The Riemann Hypothesis: The Greatest Unsolved Problem in Mathematics by Karl Sabbagh. For a rigorous mathematical treatise, if you are so inclined, you can read Riemann's Zeta Function by Harold M. Edwards. Also read about my aborted attempt to read Stalking the Riemann Hypothesis by Dan Rockmore.
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