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The aliquot sum function can be used to characterize several notable classes of numbers: 1 is the only number whose aliquot sum is 0. A number is prime if and only if its aliquot sum is 1. [1] The aliquot sums of perfect, deficient, and abundant numbers are equal to, less than, and greater than the number itself respectively. [1]
The aliquot sequence starting with a positive integer k can be defined formally in terms of the sum-of-divisors function σ 1 or the aliquot sum function s in the following way: [1] = = = > = = = If the s n-1 = 0 condition is added, then the terms after 0 are all 0, and all aliquot sequences would be infinite, and we can conjecture that all aliquot sequences are convergent, the limit of these ...
Aliquot of a sample, in chemistry and other sciences, a precise portion of a sample or total amount of a liquid (e.g. precisely 25 mL of water taken from 250 mL); Aliquot in pharmaceutics, a method of measuring ingredients below the sensitivity of a scale by proportional dilution with inactive known ingredients
The sum of proper divisors of a number is called its aliquot sum, so a perfect number is one that is equal to its aliquot sum. Equivalently, a perfect number is a number that is half the sum of all of its positive divisors; in symbols, σ 1 ( n ) = 2 n {\displaystyle \sigma _{1}(n)=2n} where σ 1 {\displaystyle \sigma _{1}} is the sum-of ...
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.
The "dilution factor" is an expression which describes the ratio of the aliquot volume to the final volume. Dilution factor is a notation often used in commercial assays. For example, in solution with a 1/5 dilution factor (which may be abbreviated as x5 dilution ), entails combining 1 unit volume of solute (the material to be diluted) with ...
In mathematics, sociable numbers are numbers whose aliquot sums form a periodic sequence.They are generalizations of the concepts of perfect numbers and amicable numbers.The first two sociable sequences, or sociable chains, were discovered and named by the Belgian mathematician Paul Poulet in 1918. [1]
The aliquot sum s(n) of n is the sum of the proper divisors (that is, the divisors excluding n itself, OEIS: ... is 1. Thus we can calculate ...