Betrothed numbers or quasi-amicable numbers are two positive integers such that the sum of the proper divisors of either number is one more than the value of the other number. In other words, (m, n) are a pair of betrothed numbers if s(m) = n + 1 and s(n) = m + 1, where s(n) is the aliquot sum of n: an equivalent condition is that σ(m) = σ(n) = m + n + 1, where σ denotes the sum-of-divisors function.
The first few pairs of betrothed numbers (sequence A005276 in the OEIS) are: (48, 75), (140, 195), (1050, 1925), (1575, 1648), (2024, 2295), (5775, 6128).
All known pairs of betrothed numbers have opposite parity. Any pair of the same parity must exceed 1010.
Betrothednumbers or quasi-amicable numbers are two positive integers such that the sum of the proper divisors of either number is one more than the value...
Brian Clegg. Amicable numbers are mentioned in the 2020 novel Apeirogon by Colum McCann. Betrothednumbers (quasi-amicable numbers) Amicable triple - Three-number...
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mathematics, the natural numbers are the numbers 0, 1, 2, 3, etc., possibly excluding 0.[under discussion] Some define the natural numbers as the non-negative...
even perfect numbers are of this form. This is known as the Euclid–Euler theorem. It is not known whether there are any odd perfect numbers, nor whether...
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such as the powers of 2. Betrothednumbers relate to quasiperfect numbers like amicable numbers relate to perfect numbers. Hagis, Peter; Cohen, Graeme...
equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The nth triangular number is...
amicable numbers? Are there infinitely many amicable numbers? Are there infinitely many betrothednumbers? Are there infinitely many Giuga numbers? Does...
different sets of numbers, generalizing from triangular numbers to different shapes (polygonal numbers) and different dimensions (polyhedral numbers). The term...
sum dynamics Abundant number Almost perfect number Amicable number Betrothednumbers Deficient number Quasiperfect number Perfect number Sociable number...
In combinatorial mathematics, the Catalan numbers are a sequence of natural numbers that occur in various counting problems, often involving recursively...
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In mathematics, the Euler numbers are a sequence En of integers (sequence A122045 in the OEIS) defined by the Taylor series expansion 1 cosh t = 2 e...
integer is composite, prime, or the unit 1, so the composite numbers are exactly the numbers that are not prime and not a unit. For example, the integer...
when written in that base. Harshad numbers in base n are also known as n-harshad (or n-Niven) numbers. Harshad numbers were defined by D. R. Kaprekar, a...
natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite...
Since the aliquot sums of prime numbers equal 1, all prime numbers are deficient. More generally, all odd numbers with one or two distinct prime factors...
square numbers are a type of figurate numbers (other examples being cube numbers and triangular numbers). In the real number system, square numbers are non-negative...
absolute test of primality. The Carmichael numbers form the subset K1 of the Knödel numbers. The Carmichael numbers were named after the American mathematician...
used meanings. 5-smooth numbers are also called regular numbers or Hamming numbers; 7-smooth numbers are also called humble numbers, and sometimes called...
of Stirling numbers of the second kind. Identities linking the two kinds appear in the article on Stirling numbers. The Stirling numbers of the second...
numbers that are not square-free, the factorization is written without exponents, writing the repeated factor as many times as needed. Smith numbers were...
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Fibonacci sequence. Individual numbers in the Lucas sequence are known as Lucas numbers. Lucas numbers and Fibonacci numbers form complementary instances...
OEIS). Numbers of the form Mn = 2n − 1 without the primality requirement may be called Mersenne numbers. Sometimes, however, Mersenne numbers are defined...
non-negative integer that has an even number of 1s in its binary expansion. These numbers give the positions of the zero values in the Thue–Morse sequence, and for...
the OEIS). Palindromic numbers receive most attention in the realm of recreational mathematics. A typical problem asks for numbers that possess a certain...
any smaller positive integer. The first ten superior highly composite numbers and their factorization are listed. For a superior highly composite number...
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