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erdős #1053 · multiply perfect numbers

← #1052 · #1054 → (packet.json; erdosproblems.com)

Call a number $k$ -perfect if $σ (n) = k n$ , where $σ (n)$ is the sum of the divisors of $n$ . Must $k = o (lo g lo g n)$ ?

Worked, still open.

number theory · open · 0 attempts

use this record

vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

evidence

unverified AI candidates (2)

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

This is **open** (it’s an Erdős problem).

candidate solution ↗

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.

candidate solution ↗

oeis

A007539 — a(n) = first n-fold perfect (or n-multiperfect) number.1,6,120,30240,14182439040,154345556085770649600,141310897947438348259849402738485523264343544818565120000

links

multiply perfect numbers · reference

perfect number · reference

this page · link

… 1 more

Create a formalisation here · link

status

open

finding.noted · reviewer:will-blair · 1 day

renders the record as of vev_d199cb2e · 1,338 events · hub