HighlyCompositeNumbers

The highly composite numbers $1, 2, 4, 6, 12, 24, …$ -- integers with more divisors than any smaller one -- as a lazy indexed collection.

OEISA002182↗

HighlyCompositeNumbersthe $n$ with $\tau(n) > \tau(m)$ for every $m < n$, an infinite indexed collection.

Domain: Collections

Details

• A lazy indexed collection: $Count(HighlyCompositeNumbers) = +\infty$ ($n!$'s divisor count strictly increases with $n$), and $At$ unranks the $k$-th by scanning forward, keeping a running record of the largest divisor count seen so far.
• Ramanujan's sequence, OEIS A002182.
• Membership goes through Element: $Element(12, HighlyCompositeNumbers)$ is true ($\tau(12) = 6$, a new record over $1..11$), $Element(18, HighlyCompositeNumbers)$ is false ($\tau(18) = 6$, not a new record).

Enumeration

Examples

1 more kept as data, checked against the oracles

About

Examples	1
Crosswalk	OEIS

See also: Count, At, Element, SuperabundantNumbers