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  2. Betrothed numbers - Wikipedia

    en.wikipedia.org/wiki/Betrothed_numbers

    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 ...

  3. Sociable number - Wikipedia

    en.wikipedia.org/wiki/Sociable_number

    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 ...

  4. Homotopy group - Wikipedia

    en.wikipedia.org/wiki/Homotopy_group

    For the corresponding definition in terms of spheres, define the sum + of maps ,: to be composed with h, where is the map from to the wedge sum of two n-spheres that collapses the equator and h is the map from the wedge sum of two n-spheres to X that is defined to be f on the first sphere and g on the second.

  5. Ruth–Aaron pair - Wikipedia

    en.wikipedia.org/wiki/Ruth–Aaron_pair

    (The lesser of each pair is listed in OEIS: A039753). Any Ruth–Aaron pair of square-free integers belongs to both lists with the same sum of prime factors. The intersection also contains pairs that are not square-free, for example (7129199, 7129200) = (7×11 2 ×19×443, 2 4 ×3×5 2 ×13×457).

  6. Amicable numbers - Wikipedia

    en.wikipedia.org/wiki/Amicable_numbers

    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.

  7. Friendly number - Wikipedia

    en.wikipedia.org/wiki/Friendly_number

    The smallest friendly number is 6, forming for example, the friendly pair 6 and 28 with abundancy σ(6) / 6 = (1+2+3+6) / 6 = 2, the same as σ(28) / 28 = (1+2+4+7+14+28) / 28 = 2. The shared value 2 is an integer in this case but not in many other cases. Numbers with abundancy 2 are also known as perfect numbers. There are several unsolved ...

  8. Karyotype - Wikipedia

    en.wikipedia.org/wiki/Karyotype

    The basic number of chromosomes in the somatic cells of an individual or a species is called the somatic number and is designated 2n. In the germ-line (the sex cells) the chromosome number is n (humans: n = 23). [4] [5] p28 Thus, in humans 2n = 46. So, in normal diploid organisms, autosomal chromosomes are present in two copies.

  9. (B, N) pair - Wikipedia

    en.wikipedia.org/wiki/(B,_N)_pair

    A (B, N) pair is a pair of subgroups B and N of a group G such that the following axioms hold: G is generated by B and N. The intersection, T, of B and N is a normal subgroup of N. The group W = N/T is generated by a set S of elements of order 2 such that If s is an element of S and w is an element of W then sBw is contained in the union of ...

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