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Topic: Hyperperfect number

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	What's special about this number? (6)
		is a triangular number: 1 + 2 + 3 + … + 19 + 20 + 21
		is the number of 7 by 7 symmetric permutation matrices.
		is a deficient number, and the number of planar partitions of 12.
	www.archimedes-lab.org /numbers/Num201_500.html (2496 words)

	TeluguPeople.com - Articles (Site not responding. Last check: 2007-11-07)
		22 is the number of partitions of 8.
		101 is the number of partitions of 13.
		231 is the number of partitions of 16.
	www.telugupeople.com /discussion/article.asp?id=24159 (16335 words)

	Интересные числа 2
		is the number of planar partitions of 17.
		is the number of planar partitions of 18.
		is the number of planar partitions of 19.
	arbuz.uz /z_numbers2.html (3643 words)

	Интересные числа на Арбузе (1)
		is the number of planar partitions of 10.
		is the number of planar partitions of 11.
		is the number of planar partitions of 12.
	www.arbuz.uz /z_numbers1.html (3969 words)

	What's Special About This Number?
		is the number of planar partitions of 10.
		is the number of planar partitions of 11.
		is the number of planar partitions of 12.
	www.stetson.edu /~efriedma/numbers.html (7292 words)

	Perfect number Summary
		In mathematics, a perfect number is defined as an integer which is the sum of its proper positive divisors, that is, the sum of the positive divisors not including the number.
		Numbers where the sum is less than the number itself are called deficient, and where it is greater than the number, abundant.
		By definition, a perfect number is a fixed point of the restricted divisor function s(n) = σ(n) − n, and the aliquot sequence associated with a perfect number is a constant sequence.
	www.bookrags.com /Perfect_number (1658 words)

	Perfect number - ExampleProblems.com
		In mathematics, a perfect number is defined as an integer which is the sum of its proper positive divisors, excluding itself.
		Numbers where the sum is less than twice the number itself are called deficient, and where it is greater than twice the number, abundant.
		A pair of numbers which are the sum of each other's proper divisors are called amicable, and larger cycles of numbers are called sociable.
	www.exampleproblems.com /wiki/index.php/Perfect_number (846 words)

	A Study of Hyperperfect Numbers
		Hyperperfect numbers are another generalization of perfect numbers, not to be confused with the better known multiply perfect, multiperfect, or k-fold perfect numbers.
		Unless otherwise noted, n denotes a hyperperfect number, k the index of perfection, p, q and r are odd primes with p
		All known hyperperfect numbers with exactly two distinct prime factors are one of these two forms, but hyperperfect numbers with more than two distinct prime factors exist which are not of these forms.
	www.emis.de /journals/JIS/VOL3/mccranie.html (2283 words)

	Prime number
		The study of prime numbers is part of number theory, the branch of mathematics which encompasses the study of natural numbers.
		For a long time, prime numbers were thought as having no possible application outside of number theory; this changed in the 1970s when the concepts of public-key cryptography were invented, in which prime numbers formed the basis of the first algorithms such as the RSA cryptosystem algorithm.
		For a long time, number theory in general, and the study of prime numbers in particular, was seen as the canonical example of pure mathematics, with no applications outside of the self-interest of studying the topic.
	www.tocatch.info /en/Prime_number.htm (5755 words)

	Straight Dope Staff Report: What's the story on perfect numbers?
		Perfect numbers are a holdover from the days of the Pythagoreans, when mathematicians were mystics as much as anything else and put a lot more stock in coincidence.
		There are also amicable numbers, sociable numbers, harmonic numbers, hyperperfect numbers, infinitary perfect numbers, unitary perfect numbers, super unitary perfect numbers, superperfect numbers, sublime numbers, and weird numbers--all of which satisfy some quirky condition or another.
		For example, sublime numbers have a perfect number of divisors, and the sum of their divisors is itself perfect.
	www.straightdope.com /mailbag/mperfectnumbers.html (683 words)

	Hyperperfect number
		In mathematics, a k-hyperperfect number (sometimes just called hyperperfect number) is a natural number n for which the equality n = 1 + k(σ(n) − n − 1) holds, where σ(n) is the divisor function (i.e., the sum of all positive divisors of n).
		The first few numbers in the sequence of k-hyperperfect numbers are 6, 21, 28, 301, 325, 496,...
		Daniel Minoli, W. Nakamine, Mersenne Numbers Rooted On 3 For Number Theoretic Transforms, 1980 IEEE International Conf.
	publicliterature.org /en/wikipedia/h/hy/hyperperfect_number.html (325 words)

	Conspiracy Knowledge Base (Site not responding. Last check: 2007-11-07)
		Number types that differentiate a number from others because of a characteristic not directly seen in the number's representation don't fit here.
		Types: * Prime number * Algebraic number * Transcendental number * Square number Odd number: An integer that is not a multiple of two.
		Harshad number: * Niven number Abundant number: * Excessive number Almost perfect number: * Slightly defective number Deficient number: * Defective number VR number: - A "visual representation" number which is a sum of some simple Function of its digits.
	gussan.freehostia.com /ckb/out/___m/number.htm (325 words)

	tingilinde: take a number ...
		92 is the number of different arrangements of 8 non-attacking queens on an 8x8 chessboard.
		352 is the number of different arrangements of 9 non-attacking queens on an 9x9 chessboard.
		1255 is the number of partitions of 23.
	tingilinde.typepad.com /starstuff/2005/11/significant_int.html (12385 words)

	Perfect Number -- from MathWorld
		Perfect numbers were deemed to have important numerological properties by the ancients, and were extensively studied by the Greeks, including Euclid.
		Perfect numbers are also intimately connected with a class of numbers known as Mersenne primes, which are prime numbers of the form
		It is known that all even perfect numbers (except 6) end in 16, 28, 36, 56, 76, or 96 (Lucas 1891) and have digital root 1.
	users.skynet.be /fa956617/math/topics/PerfectNumber.html (710 words)

	Hyperperfect number (Site not responding. Last check: 2007-11-07)
		In mathematics, a k-hyperperfect number (sometimes just called hyperperfect number) is a natural number n for which the equality n = 1 + k(Ï(n) â’ n â’ 1) holds, where Ï(n) is the divisor function (i.e., the sum of all positive divisors of n).
		A number is perfect iff it is 1-hyperperfect.
		The first few numbers in the sequence of k-hyperperfect numbers are 6, 21, 28, 301, 325, 496,...
	www.abcworld.net /Hyperperfect_number.html (318 words)

	The On-Line Encyclopedia of Integer Sequences
		Minoli, D. "Issues in Nonlinear Hyperperfect Numbers." Math.
		a(n)=m(sigma(a(n))-a(n)-1)+1 for some m>1, and a(n) is a semiprime with the same number of digits in each prime factor.
		a(2) = 697 because 697 is a 12-hyperperfect number, A028500(2), and is a brilliant number because 697 = 17 * 41.
	www.research.att.com /~njas/sequences/A100713 (169 words)

	Amazon.com: "hyperperfect numbers": Key Phrase page (Site not responding. Last check: 2007-11-07)
		Bear 12171 have generalized the concept of perfect num- her, by introducing the hyperperfect numbers.
		Hyperperfect numbers are expected to have applications in cryptology and signal pro- cessing transforms [r080, r265-r272].
		For example this author cointroduced the concept of hyperperfect numbers in the early 1970s (see Figure 3.11), a "nice" generalization of the concept of a perfect number that is now...
	www.amazon.com /phrase/hyperperfect-numbers (339 words)

	The On-Line Encyclopedia of Integer Sequences
		Daniel Minoli, Issues in non-linear hyperperfect numbers, Math.
		Daniel Minoli and Robert Bear, Hyperperfect Numbers, PME Journal, Fall 1975, pp.
		J. McCranie, A study of hyperperfect numbers, J. Int.
	www.research.att.com /~njas/sequences/A007593 (164 words)

	math lessons - Category:Number theory
		Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers and contains many open problems that are easily understood even by non-mathematicians.
		More generally, the field has come to be concerned with a wider class of problems that arose naturally from the study of integers.
		Number theory may be subdivided into several fields according to the methods used and the questions investigated.
	www.mathdaily.com /lessons/Category:Number_theory (102 words)

	Future Projects
		Furthermore a large number of preprints in mathematics and physics are available from web sites such as the LANL eprint arXiv.
		There are a number of sequences concerned with counting polyominoes of various kinds where the description needs to be made more precise.
		In a number of cases the references for a sequence just give a volume and page number but not the author or title, etc. (for a typical example see A033874 - there are lots more like this).
	www.research.att.com /~njas/sequences/future.html (3118 words)

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