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Topic: Deficient number

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	PlanetMath: deficient number
		All prime numbers are deficient, since 1 is their only proper divisor.
		Given a pair of amicable numbers, the greater of the two is deficient.
		This is version 1 of deficient number, born on 2006-04-25.
	planetmath.org /encyclopedia/DeficientNumber.html (124 words)

	Station Information - Deficient number
		In mathematics, a deficient number (also sometimes called a defective number) is a number n for which the sum of all its positive divisors (including n, the divisor function, σ(n)) is less than 2 n ; the value 2 n - σ(n) is sometimes called the deficiency of n.
		Deficient numbers were first introduced in Nicomachus' Introductio Arithmetica (circa 100).
		An infinite number of both even and odd deficient numbers exist; for example, all prime numbers, prime powers and all proper divisors of deficient or perfect numbers are deficient.
	www.stationinformation.com /encyclopedia/d/de/deficient_number.html (0 words)

	Math Forum: Ask Dr. Math FAQ: Glossary of Numbers
		A happy number is a number for which the sum of the squares of the digits eventually equals 1.
		A polygonal number is the number of equally spaced dots needed to draw a polygon.
		A triangular number is the number of dots needed to draw a triangle.
	mathforum.org /dr.math/faq/faq.number.glossary.html (1533 words)

	Deficient number - Wikipedia, the free encyclopedia
		In mathematics, a deficient number or defective number is a number n for which σ ( n) < 2 n.
		Deficient numbers were first introduced in Nicomachus ' Introductio Arithmetica (circa 100).
		prime numbers, all prime powers and all proper divisors of deficient or perfect numbers are deficient.
	en.wikipedia.org /wiki/Deficient_number (0 words)

	Divisor Tables for the Integers 101 to 200
		Count(d(N)) is the number of positive divisors of n, including 1 and n itself.
		A Deficient Number is greater than the sum of its proper divisors; that is, s(N)
		A Perfect Number equals the sum of its proper divisors; that is, s(N)=n.
	www.positiveintegers.org /IntegerTables/101-200 (499 words)

	Abundant number (Site not responding. Last check: 2007-10-31)
		In mathematics, an abundant number (also sometimes called an excessive number) is a number n for which the sum of all its positive divisors (including n, the divisor function, σ(n)) is greater than 2 n ; the value σ(n) - 2 n is sometimes called the abundance of n.
		An infinite number of both even and odd abundant numbers exist (for example, all multiples of 12 and all odd multiples 945 are abundant); furthermore, every proper multiple of a perfect number and every multiple of an abundant number is abundant.
		An abundant number which is not a semiperfect number is called a weird number ; an abundant number with abundance 1 is called a quasiperfect number.
	www.enlightenweb.net /a/ab/abundant_number.html (0 words)

	The Prime Glossary: deficient number (Site not responding. Last check: 2007-10-31)
		, with p any prime and k > 0, is deficient.
		Also if n is any perfect number, and d divides n (where 1 < d < n), then d is deficient.
		Deficient and abundant numbers were first so named in Nicomachus' Introductio Arithmetica (c.
	primes.utm.edu /glossary/page.php?sort=DeficientNumber (93 words)

	Perfect number
		A perfect number is an integer which is the sum of its proper positive divisors ( factors), not including the number itself.
		Nowadays, prime numbers generated by the formula are known as Mersenne primes, after the seventeenth-century monk, Marin Mersenne, who studied number theory and perfect numbers.
		Numbers where the sum is less than the number itself are called deficient, and where it is greater, abundant ; these terms, together with perfect itself, come from Greek numerology.
	news-server.org /p/pe/perfect_number.html (0 words)

	abundant number : Definition from the Online Dictionary at Datasegment.com
		Imperfect number (Math.), a number either greater or less than the sum of its several divisors; in the former case, it is called also a defective number ; in the latter, an abundant number.
		Imperfect power (Math.), a number which can not be produced by taking any whole number or vulgar fraction, as a factor, the number of times indicated by the power; thus, 9 is a perfect square, but an imperfect cube.
		This is opposed to a deficient number, as 14, whose aliquot parts are 1, 2, 7, the sum of which is 10; and to a perfect number, which is equal to the sum of its aliquot parts, as 6, whose aliquot parts are 1, 2., 3.
	onlinedictionary.datasegment.com /word/Abundant+number (0 words)

	Station Information - Semiperfect number
		In mathematics, a semiperfect number (also called a pseudoperfect number) is a natural number n that is equal to the sum of all or some of its proper divisors (the divisor function σ ( n)).
		The first few semiperfect numbers are 6, 12, 18, 20, 24, 28, 30, 36, 40,...
		Semiperfect numbers that are equal to the sum of all their proper divisors are called perfect number ; an abundant number which is not semiperfect is called a weird number.
	www.stationinformation.com /encyclopedia/s/se/semiperfect_number.html (0 words)

	Abundant number - Wikipedia, the free encyclopedia
		In mathematics, an abundant number or excessive number is a number n for which σ ( n) > 2 n.
		Abundant numbers were first introduced in Nicomachus ' Introductio Arithmetica (circa 100).
		An abundant number which is not a semiperfect number is called a
	en.wikipedia.org /wiki/Abundant_number (0 words)

	special number (Site not responding. Last check: 2007-10-31)
		It is an odd number, a number that is not divisible by 2.
		It is a prime number: a number that is a multiple of only1 and itself.
		It is a deficient number: a number whose proper factors add up to less than the number itself.
	www2.newton.mec.edu /%7Eken_waldman/special%20number (0 words)

	Versatile Numbers-Versatile Economics
		The whole of number has every possible division, and the number 5040 can be divided by exactly fifty-nine divisors [sixty including itself], and ten of these proceed without interval from one to ten; this will furnish numbers for war and peace, and for all contracts and dealing, including taxes and divisions of the land.
		number as a number whose number of divisors exceed that of all its predecessors." This is the same as a versatile number.
		Versatile Numbers: 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840,...
	www.earth360.com /math-versatile.html (0 words)

	Deficient number (Site not responding. Last check: 2007-10-31)
		Deficient number s were first introduced in Nicomachus' Introductio Arithmetica (circa 100).
		The first few deficient number s are 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13,...
		An infinite number of both even and odd deficient number s exist; for example, all prime number s, prime powers and all proper divisors of deficient or perfect number s are deficient.
	www.portaljuice.com /deficient_number.html (0 words)

	Number page (Site not responding. Last check: 2007-10-31)
		A deficient number is lacking in the sense that the sum of its proper factors (all its positive factors excluding itself) is less than the number itself.
		For example, the number two was associated with "opinion"; four was associated with "justice"; the number five was associated with "marriage" since it was the union of the first even number, 2, and what they considered to be the first odd number, 3.
		The number one was not considered to be a number at all, but was thought of as the divine generator of all numbers.
	www.intermath-uga.gatech.edu /tweb/gwin1-01/apley/Dictionary/Number/number.html (0 words)

	Number and Operation Session 6: Homework
		A number is called a perfect number if the sum of all of its factors is equal to twice the value of the number.
		An abundant number is one in which the sum of its factors is greater than twice the number.
		A deficient number is one in which the sum of its factors is less than twice the number.
	www.learner.org /channel/courses/learningmath/number/session6/part_h/homework.html (0 words)

	Problem A: Deficient, Perfect, and Abundant
		For each positive integer in the input, the output consists of a series of numbers formed as a digit is deleted and subtracted, followed by a message indicating whether or not the original number is divisible by 11.
		A pair of sequences is preceded by a number on a single line indicating the number of elements in the sequences.
		Numbers in a sequence are separated by a space, and each sequence is on a single line by itself.
	applewoodheights.peelschools.org /tech/craigen/ccc/1996problems.htm (0 words)

	Fascinating Triangular Numbers By Shyam Sunder Gupta (Site not responding. Last check: 2007-10-31)
		Numbers such that d(n), the number of divisors of n, is greater than for any smaller n are called highly composite numbers.
		Numbers such that s(n), the sum of aliquot divisors of n, is greater than n are called Abundant numbers.
		Numbers such that s(n), the sum of aliquot divisors of n, is less than n are called Deficient numbers.
	www.shyamsundergupta.com /triangle.htm (0 words)

	Number Theory(Prime Time) (Site not responding. Last check: 2007-10-31)
		near-perfect number: a number whose sum of its proper factors is one less than the number itself.
		perfect number: a number whose sum of its proper factors is equal to the number itself.
		symmetric primes: prime numbers which are the same distance away from a given number (using the smaller prime as the first number in a number line and the larger prime as the last number, find the median/add the two primes and divide by 2 to find the given number)
	teach.beavton.k12.or.us /~gail_hjorth/F0001F976/S0553C081 (0 words)

	InterMath \| Investigations \| Number Concept (Site not responding. Last check: 2007-10-31)
		An abundant number is a positive integer in which the sum of all its factors, other than the number itself, is greater than the number.
		A deficient number is a number in which the sum of all its factors, other than the number itself, is less than the number.
		A perfect number is a number in which the sum of all its factors, other than the number itself, equals the number.
	www.intermath-uga.gatech.edu /topics/nmcncept/integers/a13.htm (0 words)

	Analys - Carbohydrate deficient transferrin / total number of analyses (Site not responding. Last check: 2007-10-31)
		It is possible to diagnose alcoholism in primary care by sending a serum to a hospital laboratory for determination of a protein formed in the liver: carbohydrate-deficient transferrin (CDT).
		A number of studies show that carbohydrate-deficient transferrin (CDT) is a superior biochemical indicator of long-lasting high intake of alcohol.
		The results show a sensitivity of92 percent at a consumption of 50-80 grams of alcohol per 24 hour-period during at least one week whereas specificity is given as 87 percent.
	www.svls.se /sektioner/sfkk/keynumb/a-519.htm (0 words)

	Primitive semiperfect number (Site not responding. Last check: 2007-10-31)
		In mathematics, a primitive semiperfect number (also called a primitive pseudoperfect number, irreducible semiperfect number or irreducible pseudoperfect number) is a natural number that has no semiperfect proper divisor.
		The first few primitive semiperfect numbers are 6, 20, 28, 88, 104, 272, 304, 350,...
		It has been shown that there exist infinitely many odd primitive semiperfect numbers, as well as infinitely many primitive semiperfect numbers that are not harmonic divisor numbers.
	www.sciencedaily.com /encyclopedia/primitive_semiperfect_number (0 words)

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