WeirdNumbers

The weird numbers $70, 836, 4030, …$ -- abundant but not semiperfect -- as a lazy indexed collection.

OEISA006037↗mathlib4Nat.Weird↗

WeirdNumbersthe abundant $n$ with no proper-divisor subset summing to $n$, an infinite indexed collection.

Domain: Collections

Details

• A lazy indexed collection: $Count(WeirdNumbers) = +\infty$ (infinitely many are known to exist), and $At$ unranks the $k$-th by scanning forward, testing $\sigma(n) - n > n$ and then a subset-sum search over $n$'s proper divisors.
• OEIS A006037. $70$ is the smallest: its proper divisors $1, 2, 5, 7, 10, 14, 35$ sum past $70$ but no subset of them sums to exactly $70$.
• Membership goes through Element: $Element(70, WeirdNumbers)$ is true, $Element(12, WeirdNumbers)$ is false (abundant, but semiperfect).

Enumeration

Examples

1 more kept as data, checked against the oracles

About

Examples	1
Crosswalk	OEISmathlib4

See also: Count, At, Element, AbundantNumbers, SemiperfectNumbers