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[1] [2] For example, 20 is a primitive abundant number because: The sum of its proper divisors is 1 + 2 + 4 + 5 + 10 = 22, so 20 is an abundant number. The sums of the proper divisors of 1, 2, 4, 5 and 10 are 0, 1, 3, 1 and 8 respectively, so each of these numbers is a deficient number. The first few primitive abundant numbers are:
A Fourier series (/ ˈ f ʊr i eɪ,-i ər / [1]) is an expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series. [2] By expressing a function as a sum of sines and cosines, many problems involving the function become easier to analyze because trigonometric functions are ...
where ξ is the Iribarren number, is the angle of the seaward slope of a structure, H is the wave height, L 0 is the deep-water wavelength, T is the period and g is the gravitational acceleration. Depending on the application, different definitions of H and T are used, for example: for periodic waves the wave height H 0 at deep water or the ...
The only odd practical number is 1, because if is an odd number greater than 2, then 2 cannot be expressed as the sum of distinct divisors of . More strongly, Srinivasan (1948) observes that other than 1 and 2, every practical number is divisible by 4 or 6 (or both).
They do not represent a single number or a single category. For instance, if P ( X = x ) {\displaystyle P(X=x)} is written, then it represents the probability that a particular realisation of a random variable (e.g., height, number of cars, or bicycle colour), X , would be equal to a particular value or category (e.g., 1.735 m, 52, or purple ...
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 ...
In computational number theory, the Lucas test is a primality test for a natural number n; it requires that the prime factors of n − 1 be already known. [ 1 ] [ 2 ] It is the basis of the Pratt certificate that gives a concise verification that n is prime.
Contrast the term primitive notion, which is a core concept not defined in terms of other concepts. Primitive notions are used as building blocks to define other concepts. Contrast also the term undefined behavior in computer science, in which the term indicates that a function may produce or return any result, which may or may not be correct.