A unitary divisor of $n$ is $d\mid n$ such that $(d,n/d)=1$. A number $n\ge 1$ is a unitary perfect number if it is the sum of its unitary divisors (aside from $n$ itself).Are there only finite many unitary perfect numbers?

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

Let [ \sigma^*(n)=\sum_{\substack{d\mid n\(d,n/d)=1}} d ] be the **sum of the unitary divisors** of $n$. Then $n$ is *unitary perfect* exactly when the sum of the **proper** unitary divisors is $n$, i.e. [ \sigma^*(n)=2n. ]

llm-hunter · codex 5.2 extra high, gpt pro 5.2 · unverified

2 LLM attack(s) recorded (codex 5.2 extra high, gpt pro 5.2); unverified.