# abundant number

abundant number
noun
: an imperfect number that is less than the sum of all its divisors (as 12)

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Math.
a positive number that is less than the sum of all positive integers that are submultiples of it, as 12, which is less than the sum of 1, 2, 3, 4, and 6. Cf. deficient number, perfect number.

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abundant number,
a whole number whose divisors have a sum greater than twice this number. The number 18 is an abundant number because the sum of its divisors (18, 9, 6, 3, 2, 1) is greater than 2 × 18.

Useful english dictionary. 2012.

### Look at other dictionaries:

• 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.… …   The Collaborative International Dictionary of English

• Abundant number — Number Num ber (n[u^]m b[ e]r), n. [OE. nombre, F. nombre, L. numerus; akin to Gr. no mos that which is dealt out, fr. ne mein to deal out, distribute. See {Numb}, {Nomad}, and cf. {Numerate}, {Numero}, {Numerous}.] 1. That which admits of being… …   The Collaborative International Dictionary of English

• Abundant number — In mathematics, an abundant number or excessive number is a number n for which σ ( n ) > 2 n . Here σ ( n ) is the sum of divisors function: the sum of all positive divisors of n , including n itself. The value σ ( n ) − 2 n is called the… …   Wikipedia

• abundant number — Imperfect Im*per fect, a. [L. imperfectus: pref. im not + perfectus perfect: cf. F imparfait, whence OE. imparfit. See {Perfect}.] 1. Not perfect; not complete in all its parts; wanting a part; deective; deficient. [1913 Webster] Something he… …   The Collaborative International Dictionary of English

• abundant number — noun A number that is less than the sum of all of its divisors except itself. The factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30, and 1 + 2 + 3 + 5 + 6 + 10 + 15 = 42, which is greater than 30, so 30 is an abundant number. Syn: excessive number …   Wiktionary

• abundant number — Math. a positive number that is less than the sum of all positive integers that are submultiples of it, as 12, which is less than the sum of 1, 2, 3, 4, and 6. Cf. deficient number, perfect number. * * * …   Universalium

• Colossally abundant number — In mathematics, a colossally abundant number (sometimes abbreviated as CA) is a natural number that, in some rigorous sense, has a lot of divisors. Formally, a number n is colossally abundant if and only if there is an ε > 0 such… …   Wikipedia

• Highly abundant number — In mathematics, a highly abundant number is a natural number where the sum of its divisors (including itself) is greater than the sum of the divisors of any natural number less than it.Highly abundant numbers and several similar classes of… …   Wikipedia

• 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. [1913… …   The Collaborative International Dictionary of English

• Number — Num ber (n[u^]m b[ e]r), n. [OE. nombre, F. nombre, L. numerus; akin to Gr. no mos that which is dealt out, fr. ne mein to deal out, distribute. See {Numb}, {Nomad}, and cf. {Numerate}, {Numero}, {Numerous}.] 1. That which admits of being counted …   The Collaborative International Dictionary of English