Definition of Abundant number. Meaning of Abundant number. Synonyms of Abundant number

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Definition of Abundant number

Abundant number
Number Num"ber, n. [OE. nombre, F. nombre, L. numerus; akin to Gr. ? that which is dealt out, fr. ? to deal out, distribute. See Numb, Nomad, and cf. Numerate, Numero, Numerous.] 1. That which admits of being counted or reckoned; a unit, or an aggregate of units; a numerable aggregate or collection of individuals; an assemblage made up of distinct things expressible by figures. 2. A collection of many individuals; a numerous assemblage; a multitude; many. Ladies are always of great use to the party they espouse, and never fail to win over numbers. --Addison. 3. A numeral; a word or character denoting a number; as, to put a number on a door. 4. Numerousness; multitude. Number itself importeth not much in armies where the people are of weak courage. --Bacon. 5. The state or quality of being numerable or countable. Of whom came nations, tribes, people, and kindreds out of number. --2 Esdras iii. 7. 6. Quantity, regarded as made up of an aggregate of separate things. 7. That which is regulated by count; poetic measure, as divisions of time or number of syllables; hence, poetry, verse; -- chiefly used in the plural. I lisped in numbers, for the numbers came. --Pope. 8. (Gram.) The distinction of objects, as one, or more than one (in some languages, as one, or two, or more than two), expressed (usually) by a difference in the form of a word; thus, the singular number and the plural number are the names of the forms of a word indicating the objects denoted or referred to by the word as one, or as more than one. 9. (Math.) The measure of the relation between quantities or things of the same kind; that abstract species of quantity which is capable of being expressed by figures; numerical value. Abstract number, Abundant number, Cardinal number, etc. See under Abstract, Abundant, etc. In numbers, in numbered parts; as, a book published in numbers.
Abundant number
Abundant A*bun"dant, a. [OE. (h)abundant, aboundant, F. abondant, fr. L. abudans, p. pr. of abundare. See Abound.] Fully sufficient; plentiful; in copious supply; -- followed by in, rarely by with. ``Abundant in goodness and truth.' --Exod. xxxiv. 6. Abundant number (Math.), a number, the sum of whose aliquot parts exceeds the number itself. Thus, 1, 2, 3, 4, 6, the aliquot parts of 12, make the number 16. 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. Syn: Ample; plentiful; copious; plenteous; exuberant; overflowing; rich; teeming; profuse; bountiful; liberal. See Ample.

Meaning of Abundant number from wikipedia

- In number theory, an abundant number or excessive number is a positive integer for which the sum of its proper divisors is greater than the number. The...
- In number theory, a colossally abundant number (sometimes abbreviated as CA) is a natural number that, in a particular, rigorous sense, has many divisors...
- In number theory, a highly abundant number is a natural number with the property that the sum of its divisors (including itself) is greater than the sum...
- primitive abundant number is an abundant number whose proper divisors are all deficient numbers. For example, 20 is a primitive abundant number because:...
- twentieth abundant and highly abundant number (with 20 the first primitive abundant number and 70 the second). 90 is the third unitary perfect number (after...
- number (7 × 11 × 13), pentagonal number, pentatope number, palindromic number 1002 = sphenic number, Mertens function zero, abundant number, number of...
- natural number following 199 and preceding 201. 200 is an abundant number, as 265, the sum of its proper divisors, is greater than itself. The number appears...
- semiperfect number. Eighteen is the first inverted square-prime of the form p·q2. In base ten, it is a Harshad number. It is an abundant number, as the sum...
- whereas an abundant number has a sum of its proper divisors that is larger than the number itself. Primitive abundant numbers are abundant numbers whose...
- the prime 7-aliquot tree. It is the smallest primitive abundant number, and the first number to have an abundance of 2, followed by 104. 20 is the length...