In 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...

of its positive proper unitary divisors, not including the number itself. (A divisor d of a number n is a unitary divisor if d and n/d share no common factors)...

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...

In mathematics, the greatest common divisor (GCD), also known as greatest common factor (GCF), of two or more integers, which are not all zero, is the...

divisors. (A divisor d of a number n is a unitary divisor if d and n/d share no common factors.). A unitary multiply perfect number is simply a unitary multi...

evenly. Every natural number has both 1 and itself as a divisor. If it has any other divisor, it cannot be prime. This leads to an equivalent definition...

Look up unitary in Wiktionary, the free dictionary. Unitary may refer to: Unitary divisor Unitary element Unitary group Unitary matrix Unitary morphism...

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...

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...

and triplets). 90 is the third unitary perfect number (after 6 and 60), since it is the sum of its unitary divisors excluding itself, and because it...

that a m = 1 mod c {\displaystyle am=1{\bmod {c}}} , and for each unitary divisor d {\displaystyle d} of N − 1 {\displaystyle N-1} let e = N − 1 d {\displaystyle...

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...

group theorist Philip Hall (1928). A Hall divisor (also called a unitary divisor) of an integer n is a divisor d of n such that d and n/d are coprime. The...

positive integers. Accordingly it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime, or...

proper divisors, making it the smallest perfect number. It is also the only perfect number that doesn't have a digital root of 1. 6 is the first unitary perfect...

particular rigorous sense, has many divisors. Particularly, it is defined by a ratio between the number of divisors an integer has and that integer raised...

any unitary divisor of the group order (that is, a divisor coprime to its cofactor). The converse of Lagrange's theorem states that if d is a divisor of...

the sum of its positive proper divisors, that is, divisors excluding the number itself. For instance, 6 has proper divisors 1, 2 and 3, and 1 + 2 + 3 = 6...

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...

the three largest known primes. All sphenic numbers have exactly eight divisors. If we express the sphenic number as n = p ⋅ q ⋅ r {\displaystyle n=p\cdot...

smallest number with exactly 17 divisors (but there are smaller numbers with more than 17 divisors; e.g., 180 has 18 divisors) (sequence A005179 in the OEIS)...

order dividing 2 to obtain a coprime factorization of the largest odd divisor of Δ in which Δ = −4ac or Δ = a(a − 4c) or Δ = (b − 2a)(b + 2a). If the...

numbers. The canonical representations of the product, greatest common divisor (GCD), and least common multiple (LCM) of two numbers a and b can be expressed...

divisors of n {\displaystyle n} . For example, 12 is a practical number because all the numbers from 1 to 11 can be expressed as sums of its divisors...

which the sum of its proper divisors is greater than the number. The integer 12 is the first abundant number. Its proper divisors are 1, 2, 3, 4 and 6 for...

m {\displaystyle m} is the largest divisor of n {\displaystyle n} such that m 2 {\displaystyle m^{2}} is a divisor of n {\displaystyle n} . In summary...

In mathematics, Dirichlet convolution (or divisor convolution) is a binary operation defined for arithmetic functions; it is important in number theory...

Divisibility-based sets of integers Overview Integer factorization Divisor Unitary divisor Divisor function Prime factor Fundamental theorem of arithmetic Factorization...

Divisibility-based sets of integers Overview Integer factorization Divisor Unitary divisor Divisor function Prime factor Fundamental theorem of arithmetic Factorization...

Divisibility-based sets of integers Overview Integer factorization Divisor Unitary divisor Divisor function Prime factor Fundamental theorem of arithmetic Factorization...