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).

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'').

For example:

* '''12''' is ''not'' a weird number.
** It is abundant; its proper divisors '''1, 2, 3, 4, 6''' sum to '''16''' (which ''is'' > 12),
** but it ''is'' semiperfect, e.g.: &nbsp; &nbsp; '''6 + 4 + 2 == 12'''.
* '''70''' ''is'' a weird number.
** It is abundant; its proper divisors '''1, 2, 5, 7, 10, 14, 35''' sum to '''74''' (which ''is'' > 70),
** and there is no subset of proper divisors that sum to '''70'''.


;Task:
Find and display, here on this page, the first '''25''' weird numbers.


;Related tasks:
:* [[Abundant,_deficient_and_perfect_number_classifications|Abundant, deficient and perfect number classifications]]
:* [[Proper_divisors|Proper divisors]]


;See also:
:* [[oeis:A006037|OEIS: A006037 weird numbers]]
:* [[wp:weird number|Wikipedia: weird number]]
:* [http://mathworld.wolfram.com/WeirdNumber.html MathWorld: weird number]
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