Weird numbers: Difference between revisions

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]].

In other words, the sum of the [[wp:Divisor#Further_notions_and_facts|proper divisors]] of the number (divisors including 1 but not itself) of the number 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'').

E.G.* '''12''' is ''not'' a weird number. It is abundant; the proper divisors '''1, 2, 3, 4 & 6''' sum to '''16''', but it is semiperfect,

** but it ''is'' semiperfect, '''6 + 4 + 2 == 12'''.

* '''70''' ''is'' a weird number. It is abundant; the proper divisors '''1, 2, 5, 7, 10, 14 & 35''' sum to '''74''', but there is no subset

of** It is abundant; its proper divisors that'''1, 2, 5, 7, 10, 14, 35''' sum to '''7074'''.,