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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 ...
The period of the sequence, or order of the set of sociable numbers, is the number of numbers in this cycle. If the period of the sequence is 1, the number is a sociable number of order 1, or a perfect number—for example, the proper divisors of 6 are 1, 2, and 3, whose sum is again 6. A pair of amicable numbers is a set of sociable numbers of ...
Sociable numbers are the numbers in cyclic lists of numbers (with a length greater than 2) where each number is the sum of the proper divisors of the preceding number. For example, 1264460 ↦ 1547860 ↦ 1727636 ↦ 1305184 ↦ 1264460 ↦ … {\displaystyle 1264460\mapsto 1547860\mapsto 1727636\mapsto 1305184\mapsto 1264460\mapsto \dots } are ...
The Stirling numbers of the second kind can represent the total number of rhyme schemes for a poem of n lines. (,) gives the number of possible rhyming schemes for n lines using k unique rhyming syllables. As an example, for a poem of 3 lines, there is 1 rhyme scheme using just one rhyme (aaa), 3 rhyme schemes using two rhymes (aab, aba, abb ...
Number of permutations of n elements with no fixed points. ... The largest order of permutation of n ... Primary pseudoperfect numbers: 2, 6, 42, 1806, 47058 ...
A natural number is a sociable Meertens number if it is a periodic point for , where () = for a positive integer , and forms a cycle of period . A Meertens number is a sociable Meertens number with k = 1 {\displaystyle k=1} , and a amicable Meertens number is a sociable Meertens number with k = 2 {\displaystyle k=2} .
In algebraic topology, the Betti numbers are used to distinguish topological spaces based on the connectivity of n-dimensional simplicial complexes.For the most reasonable finite-dimensional spaces (such as compact manifolds, finite simplicial complexes or CW complexes), the sequence of Betti numbers is 0 from some point onward (Betti numbers vanish above the dimension of a space), and they ...
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