Betrothed numbersorquasi-amicable numbersare two positiveintegerssuch that thesumof theproper divisorsof either number is one more than the value of the other number. In other words, (m,n) are a pair of betrothed numbers ifs(m) =n+ 1 and s(n) =m+ 1, where s(n) is thealiquot sumofn:an equivalent condition is that σ(m) = σ(n) =m+n+ 1, where σ denotes thesum-of-divisors function.
The first few pairs of betrothed numbers (sequenceA005276in theOEIS) are: (48, 75), (140, 195), (1050, 1925), (1575, 1648), (2024, 2295), (5775, 6128).
All known pairs of betrothed numbers have oppositeparity.Any pair of the same parity must exceed 1010.
Quasi-sociable numbers
Quasi-sociable numbers or reduced sociable numbers are numbers whosealiquot sumsminus one form a cyclic sequence that begins and ends with the same number. They are generalizations of the concepts of betrothed numbers andquasiperfect numbers.The first quasi-sociable sequences, or quasi-sociable chains, were discovered by Mitchell Dickerman in 1997:
