Definition:Weird Number

Definition

A weird number is an abundant number which is not at the same time semiperfect.

Sequence of Weird Numbers

The sequence of weird numbers begins:

$70, 836, 4030, 5830, 7192, 7912, 9272, \ldots$

Examples of Weird Numbers

$70$ is a Weird Number

The aliquot sum of $70$ is $74$, but no subset of its aliquot parts add to $70$.

$836$ is a Weird Number

The aliquot sum of $836$ is $844$, but no subset of its aliquot parts add to $836$.

$4030$ is a Weird Number

The aliquot sum of $4030$ is $4034$, but no subset of its aliquot parts add to $4030$.

Also see

• Definition:Abundant Number
• Definition:Semiperfect Number

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $70$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $70$