29 lines
1.4 KiB
Text
29 lines
1.4 KiB
Text
In number theory, a [[wp:weird number|weird number]] is a natural number that is [[wp:abundant number|abundant]] but ''not'' [[wp:semiperfect number|semiperfect]] (and therefore not [[wp:perfect number|perfect]] either).
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In other words, the sum of the [[wp:Divisor#Further_notions_and_facts|proper divisors]] of the number (divisors including 1 but not itself) is greater than the number itself (the number is ''abundant''), but no subset of those divisors sums to the number itself (the number is not ''semiperfect'').
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For example:
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* '''12''' is ''not'' a weird number.
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** It is abundant; its proper divisors '''1, 2, 3, 4, 6''' sum to '''16''' (which ''is'' > 12),
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** but it ''is'' semiperfect, e.g.: '''6 + 4 + 2 == 12'''.
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* '''70''' ''is'' a weird number.
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** It is abundant; its proper divisors '''1, 2, 5, 7, 10, 14, 35''' sum to '''74''' (which ''is'' > 70),
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** and there is no subset of proper divisors that sum to '''70'''.
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;Task:
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Find and display, here on this page, the first '''25''' weird numbers.
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;Related tasks:
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:* [[Abundant,_deficient_and_perfect_number_classifications|Abundant, deficient and perfect number classifications]]
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:* [[Proper_divisors|Proper divisors]]
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;See also:
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:* [[oeis:A006037|OEIS: A006037 weird numbers]]
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:* [[wp:weird number|Wikipedia: weird number]]
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:* [http://mathworld.wolfram.com/WeirdNumber.html MathWorld: weird number]
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<br>
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