PerfectNumbers

The perfect numbers $6, 28, 496, 8128, …$ -- integers equal to the sum of their proper divisors -- as a lazy indexed collection.

PerfectNumbersthe

n

with

\sigma(n) = 2n

, an indexed collection of unknown count.

Domain: Collections

Details

$Count(PerfectNumbers) = NaN$ : every even perfect number is $2^{p-1}(2^p - 1)$ for a Mersenne prime exponent $p$ (Euclid–Euler), but whether any odd perfect number exists -- and so whether the family is even finite or infinite -- is open.
$At$ reads off a table of the known even perfect numbers that fit an exact JS integer ( $p = 2, 3, 5, 7, 13, 17, 19$ ); past that table it returns unevaluated rather than scanning forever, since no predicate here could safely keep searching.
OEIS A000396. Membership goes through Element: $Element(28, PerfectNumbers)$ is true, $Element(24, PerfectNumbers)$ is false (abundant, not perfect).

Enumeration

2 more kept as data, checked against the oracles

About

Examples	2
Crosswalk	OEIS mathlib4