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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
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.
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 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 ...
As an example, the number 1,264,460 is a sociable number whose cyclic aliquot sequence has a period of 4: The sum of the proper divisors of (=) is 1 + 2 + 4 + 5 + 10 + 17 + 20 + 34 + 68 + 85 + 170 + 340 + 3719 + 7438 + 14876 + 18595 + 37190 + 63223 + 74380 + 126446 + 252892 + 316115 + 632230 = 1547860,
The material may be solid, liquid, gas, a material of some intermediate characteristics such as gel or sputum, tissue, organism, or a combination of these.Even if a material sample is not countable as individual items, the quantity of the sample may still be describable in terms of its volume, mass, size, or other such dimensions.
Get the Carlsbad, CA local weather forecast by the hour and the next 10 days.
James Larkin White (July 11, 1882– April 26, 1946) was a cowboy, guano miner, cave explorer, and park ranger for the National Park Service.He is best remembered as the discoverer, early promoter and explorer of what is known today as Carlsbad Caverns in Carlsbad Caverns National Park, New Mexico.