PracticalNumbers

The practical numbers $1, 2, 4, 6, 8, 12, …$ -- integers whose divisors let every smaller integer be written as a distinct-divisor sum -- as a lazy indexed collection.

OEISA005153↗

PracticalNumbersthe $n$ where every $1 \le m \le n$ is a sum of distinct divisors of $n$, an infinite indexed collection.

Domain: Collections

Details

• A lazy indexed collection: $Count(PracticalNumbers) = +\infty$ (Saias 1997 confirmed they have positive density), and $At$ unranks the $k$-th by the classical criterion -- sorted divisors $d_1 = 1 < d_2 < … < d_j = n$, practical iff no $d_{i+1}$ exceeds $1 + \sum_{l \le i} d_l$.
• OEIS A005153.
• Membership goes through Element: $Element(12, PracticalNumbers)$ is true, $Element(10, PracticalNumbers)$ is false ($7$ isn't a sum of $10$'s divisors $\{1,2,5,10\}$).

Enumeration

Examples

1 more kept as data, checked against the oracles

About

Examples	1
Crosswalk	OEIS

See also: Count, At, Element, ArithmeticNumbers