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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 ...
A pair of amicable numbers constitutes an aliquot sequence of period 2. A related concept is that of a perfect number , which is a number that equals the sum of its own proper divisors, in other words a number which forms an aliquot sequence of period 1.
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 ...
An abundant number is a natural number n for which the sum of divisors σ(n) satisfies σ(n) > 2n, or, equivalently, the sum of proper divisors (or aliquot sum) s(n) satisfies s(n) > n. The abundance of a natural number is the integer σ(n) − 2n (equivalently, s(n) − n).
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 ...