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Quasi-sociable numbers or reduced sociable numbers are numbers whose aliquot sums minus one form a cyclic sequence that begins and ends with the same number. They are generalizations of the concepts of betrothed numbers and quasiperfect numbers. The first quasi-sociable sequences, or quasi-sociable chains, were discovered by Mitchell Dickerman ...
where n > 1 is an integer and p, q, r are prime numbers, then 2 n × p × q and 2 n × r are a pair of amicable numbers. This formula gives the pairs (220, 284) for n = 2, (17296, 18416) for n = 4, and (9363584, 9437056) for n = 7, but no other such pairs are known. Numbers of the form 3 × 2 n − 1 are known as Thabit numbers.
The selection of betrothal gifts varies by the ancestral regions of the bride and groom. [6] In cases of intermarriage between various Chinese dialect speakers, brides typically follow the groom's ancestral traditions, not the other way around. [7] The gifts are often in even number for the meaning of in couple and in pairs.
A pair of amicable numbers is a set of sociable numbers of order 2. There are no known sociable numbers of order 3, and searches for them have been made up to as of 1970. [2] It is an open question whether all numbers end up at either a sociable number or at a prime (and hence 1), or, equivalently, whether there exist numbers whose aliquot ...
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The origins of European engagement in marriage practice are found in the Jewish law (), first exemplified by Abraham, and outlined in the last Talmudic tractate of the Nashim (Women) order, where marriage consists of two separate acts, called erusin (or kiddushin, meaning sanctification), which is the betrothal ceremony, and nissu'in or chupah, [a] the actual ceremony for the marriage.
More generally, if the numbers n and σ(n) are coprime – meaning that the greatest common divisor of these numbers is 1, so that σ(n)/n is an irreducible fraction – then the number n is solitary (sequence A014567 in the OEIS). For a prime number p we have σ(p) = p + 1, which is co-prime with p.
Communities exerted pressure on people to form pair-bonds in places such as Europe; in China, society "demanded people get married before having a sexual relationship" [4] and many societies found that some formally recognized bond between a man and a woman was the best way of rearing and educating children as well as helping to avoid conflicts ...