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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 ...
For the Love of Dogs has won a number of awards. The show has won two consecutive National Television Awards for 'Most Popular Factual Entertainment Programme' in 2013 and 2014 . In 2014, it was nominated for a third National Television Award , this time under the category 'Most Popular Factual Programme', but lost out to Gogglebox . [ 4 ]
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 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 ...
Jim Jim, a Bulldog, wears a head decoration during the 149th Annual Westminster Kennel Club Dog Show at the Jacob Javits Convention Center in New York City, U.S., February 10, 2025.
[4] In a 2022 review, Melinda Houston of The Sydney Morning Herald wrote, "It's sort of a competition to see who can best train a working dog pup in just 12 months, but the more interesting face of the show is the insight into the dogs themselves, the people who breed and train them, and the farmers who work them."
In another instance of the Simpsons appearing to predict the future, a clip from the 1997 episode “The Springfield Files” was shared featuring the Red Tick Beer brewery showing that they make ...
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