number theory, a divisor function is an arithmetic function related to the divisors of an integer. When referred to as the divisor function, it counts the...
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In number theory, the divisor summatory function is a function that is a sum over the divisor function. It frequently occurs in the study of the asymptotic...
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In mathematics, a divisor of an integer n , {\displaystyle n,} also called a factor of n , {\displaystyle n,} is an integer m {\displaystyle m} that may...
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In mathematics, the greatest common divisor (GCD) of two or more integers, which are not all zero, is the largest positive integer that divides each of...
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divisors are a generalization of codimension-1 subvarieties of algebraic varieties. Two different generalizations are in common use, Cartier divisors...
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2 (section The divisor function)
has two distinct factors (itself and 1). Therefore, the number-of-divisors function d ( n ) {\displaystyle d(n)} of positive integers n {\displaystyle...
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Aliquot sum (redirect from Restricted divisor function)
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, s ( n ) = ∑ d | n , d...
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called Euler's phi function. In other words, it is the number of integers k in the range 1 ≤ k ≤ n for which the greatest common divisor gcd(n, k) is equal...
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coefficients of the Ramanujan modular form Divisor function, an arithmetic function giving the number of divisors of an integer This disambiguation page lists...
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integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime, or...
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prime-counting functions. This article provides links to functions of both classes. An example of an arithmetic function is the divisor function whose value...
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Prime number (redirect from Prime divisor)
number 1: for instance, the formulas for Euler's totient function or for the sum of divisors function are different for prime numbers than they are for 1....
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divisors of the numbers 1 to 1000. A divisor of an integer n is an integer m, for which n/m is again an integer (which is necessarily also a divisor of...
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Sphenic number (section Divisors)
exactly eight divisors. All sphenic numbers are by definition squarefree, because the prime factors must be distinct. The Möbius function of any sphenic...
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by sigma function one can mean one of the following: The sum-of-divisors function σa(n), an arithmetic function Weierstrass sigma function, related to...
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the divisor function, denotes the number of divisors of n. The term was coined by Ramanujan (1915). For example, the number with the most divisors per...
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harmonic divisor number or Ore number is a positive integer whose divisors have a harmonic mean that is an integer. The first few harmonic divisor numbers...
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Perfect number (category Divisor function)
positive divisors; in symbols, σ 1 ( n ) = 2 n {\displaystyle \sigma _{1}(n)=2n} where σ 1 {\displaystyle \sigma _{1}} is the sum-of-divisors function. This...
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Fibonacci sequence (section Prime divisors)
\ldots )=F_{\gcd(a,b,c,\ldots )}\,} where gcd is the greatest common divisor function. In particular, any three consecutive Fibonacci numbers are pairwise...
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mathematics, a natural number a is a unitary divisor (or Hall divisor) of a number b if a is a divisor of b and if a and b a {\displaystyle {\frac {b}{a}}}...
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functions with a specified divisor. The functions half and third curry the divide function with a fixed divisor. The divisor function also forms a closure by...
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if n is not square-free σk(n): the divisor function, which is the sum of the k-th powers of all the positive divisors of n (where k may be any complex number)...
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useful identities related to number-theoretic divisor sums, i.e., sums of an arithmetic function over the divisors of a natural number n {\displaystyle n} ...
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Weird number (category Divisor function)
of the proper divisors (divisors including 1 but not itself) of the number is greater than the number, but no subset of those divisors sums to the number...
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sum of all or some of its proper divisors. A semiperfect number that is equal to the sum of all its proper divisors is a perfect number. The first few...
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Deficient number (category Divisor function)
integer n for which the sum of divisors of n is less than 2n. Equivalently, it is a number for which the sum of proper divisors (or aliquot sum) is less than...
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where we have the special case identity for the generating function of the divisor function, d(n) ≡ σ0(n), given by ∑ n = 1 ∞ x n 1 − x n = ∑ n = 1 ∞ x...
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frontotemporal lobar degeneration, and chronic traumatic encephalopathy Divisor function in number theory, also denoted d or σ0 Golden ratio (1.618...), although...
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Amicable numbers (category Divisor function)
itself (see also divisor function). The smallest pair of amicable numbers is (220, 284). They are amicable because the proper divisors of 220 are 1, 2...
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Multiply perfect number (category Divisor function)
k-perfect (or k-fold perfect) if the sum of all positive divisors of n (the divisor function, σ(n)) is equal to kn; a number is thus perfect if and only...
16 KB (1,706 words) - 01:39, 16 April 2024