SuperabundantNumbers

The superabundant numbers $1, 2, 4, 6, 12, 24, …$ -- integers whose abundancy $\sigma(n)/n$ exceeds every smaller one's -- as a lazy indexed collection.

OEISA004394

SuperabundantNumbersthe

n

with

\sigma(n)/n > \sigma(m)/m

for every

m < n

, an infinite indexed collection.

Domain: Collections

Details

A lazy indexed collection: $Count(SuperabundantNumbers) = +\infty$ , and $At$ unranks the $k$ -th by scanning forward, comparing abundancy ratios by cross-multiplication (exact, no floating point) against a running record.
OEIS A004394. Every superabundant number is highly composite, but not conversely -- the two sequences share early terms and then diverge (e.g. $180$ is superabundant but not highly composite, and vice versa further out).
Membership goes through Element: $Element(4, SuperabundantNumbers)$ is true ( $\sigma(4)/4 = 7/4$ , a new record over $1..3$ ), $Element(3, SuperabundantNumbers)$ is false ( $\sigma(3)/3 = 4/3 < \sigma(2)/2 = 3/2$ ).

Enumeration

Examples

1 more kept as data, checked against the oracles

About

Examples	1
Crosswalk	OEIS

SuperabundantNumbers ​

Enumeration

Examples

SuperabundantNumbers