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Print/export Download as PDF; ... The tables below list all of the divisors of the numbers 1 to 1000. ... 11, 15, 33, 55, 165 8 288 123 deficient, composite ...
Equivalently, it is a number for which the sum of proper divisors (or aliquot sum) is less than n. For example, the proper divisors of 8 are 1, 2, and 4, and their sum is less than 8, so 8 is deficient. Denoting by σ(n) the sum of divisors, the value 2n – σ(n) is called the number's deficiency.
In number theory, the aliquot sum s(n) of a positive integer n is the sum of all proper divisors of n, that is, all divisors of n other than n itself. That is, = |,. It can be used to characterize the prime numbers, perfect numbers, sociable numbers, deficient numbers, abundant numbers, and untouchable numbers, and to define the aliquot sequence of a number.
For example, to find the Hall divisors of 60, its prime power factorization is 2 2 × 3 × 5, so one takes any product of 3, 2 2 = 4, and 5. Thus, the Hall divisors of 60 are 1, 3, 4, 5, 12, 15, 20, and 60. A Hall subgroup of G is a subgroup whose order is a Hall divisor of the order of G. In other words, it is a subgroup whose order is coprime ...
This is true in the case of 6; 6's divisors are 1,2,3, and 6, but an abundant number is defined to be one where the sum of the divisors, excluding itself, is greater than the number itself; 1+2+3=6, so this condition is not met (and 6 is instead a perfect number). However all colossally abundant numbers are also superabundant numbers. [12]
Demonstration of the practicality of the number 12. In number theory, a practical number or panarithmic number [1] is a positive integer such that all smaller positive integers can be represented as sums of distinct divisors of .
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 of the divisors of any smaller natural number. Highly abundant numbers and several similar classes of numbers were first introduced by Pillai ( 1943 ), and early work on the subject was done by ...
M = 15 The 15 perfect matchings of K 6 15 as the difference of two positive squares (in orange).. 15 is: The eighth composite number and the sixth semiprime and the first odd and fourth discrete semiprime; [1] its proper divisors are 1, 3, and 5, so the first of the form (3.q), [2] where q is a higher prime.