ArithmeticNumbers

The arithmetic numbers $1, 3, 5, 6, 7, …$ -- integers whose divisors have an integer mean -- as a lazy indexed collection.

OEISA003601↗

ArithmeticNumbersthe $n$ with $\tau(n) \mid \sigma(n)$, an infinite indexed collection.

Domain: Collections

Details

• A lazy indexed collection: $Count(ArithmeticNumbers) = +\infty$ (almost all integers are arithmetic -- the exceptions have density zero), and $At$ unranks the $k$-th by scanning forward, testing $\sigma(n) \bmod \tau(n) = 0$.
• OEIS A003601.
• Membership goes through Element: $Element(6, ArithmeticNumbers)$ is true (divisors $1,2,3,6$ average $3$), $Element(4, ArithmeticNumbers)$ is false (divisors $1,2,4$ average $7/3$).

Enumeration

Examples

1 more kept as data, checked against the oracles

About

Examples	1
Crosswalk	OEIS

See also: Count, At, Element, PracticalNumbers