SemiperfectNumbers

The semiperfect numbers $6, 12, 18, 20, …$ -- integers equal to a sum of some subset of their proper divisors -- as a lazy indexed collection.

OEISA005835↗mathlib4Nat.Pseudoperfect↗

SemiperfectNumbersthe $n$ with a proper-divisor subset summing to $n$, an infinite indexed collection.

Domain: Collections

Details

• A lazy indexed collection: $Count(SemiperfectNumbers) = +\infty$ (every perfect number is trivially semiperfect, taking the whole divisor set), and $At$ unranks the $k$-th by scanning forward, testing each candidate with a subset-sum search over its proper divisors.
• OEIS A005835.
• Membership goes through Element: $Element(12, SemiperfectNumbers)$ is true ($12 = 2 + 4 + 6$), $Element(70, SemiperfectNumbers)$ is false -- $70$ is abundant but [[WeirdNumbers|weird]].

Enumeration

Examples

1 more kept as data, checked against the oracles

About

Examples	1
Crosswalk	OEISmathlib4

See also: Count, At, Element, PerfectNumbers, WeirdNumbers