UntouchableNumbers

The untouchable numbers $2, 5, 52, 88, …$ -- integers that are no number's aliquot sum -- as a lazy indexed collection.

UntouchableNumbersthe

n

with

\sigma(m) - m \ne n

for every

m

, an infinite indexed collection.

Domain: Collections

Details

A lazy indexed collection: $Count(UntouchableNumbers) = +\infty$ (Erdős), and $At$ unranks the $k$ -th by scanning forward, testing each candidate $n$ against a sieve of aliquot sums $\sigma(m) - m$ for $m$ up to $n^2$ -- large enough to catch $m = p^2$ for a prime $p$ as big as $n - 1$ , which gives aliquot sum $1 + p = n$ .
OEIS A005114. $1$ is excluded by convention even though it's also never an aliquot sum for $m > 1$ ; the sequence starts at $2$ .
Membership goes through Element: $Element(5, UntouchableNumbers)$ is true, $Element(4, UntouchableNumbers)$ is false ( $\sigma(9) - 9 = 4$ ).

Enumeration

1 more kept as data, checked against the oracles

About

Examples	1
Crosswalk	OEIS