Let $A$ be the set of all $n$ such that $n = d_{1} + \dots + d_{k}$ with $d_{i}$ distinct proper divisors of $n$ , but this is not true for any $m ∣ n$ with $m < n$ . Does $n \in A \sum \frac{1}{n}$ converge?

Worked, still open.

number theory · open · formalized (Lean) · 0 attempts

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vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

evidence

unverified AI candidates (2)

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

Your set $A$ is exactly the set of **primitive pseudoperfect numbers** (also called *primitive semiperfect* or *irreducible semiperfect* numbers). ([OEIS][1])

candidate solution ↗

llm-hunter · gpt pro 5.2 · unverified

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

candidate solution ↗

formal

AMS 11 · open (literature)

theorem erdos_469 :
    letI A := {n : ℕ | 0 < n ∧ n.IsSumDivisors ∧ ∀ m < n, m ∣ n → ¬ m.IsSumDivisors}
    answer(sorry) ↔ Summable fun n : A ↦ 1 / (n : ℝ)

formal-conjectures/469.lean ↗

oeis

A006036 — Primitive pseudoperfect numbers.6,20,28,88,104,272,304,350,368,464,490,496,550,572,650,748,770,910,945,1184,1190,1312,1330,1376,1430,1504,1575,1610,1696 A119425 — Primitive terms of the sequence A119357, i.e., of the sequence of those values of n for which the number of distinct nonzero sums of distinct divisors of n is less than 2^tau(n) - 1.6,20,28,45,63,70,88,99,104,105,110,117,130,154,165,170,182,195,231,238,255,266,272,273,285,286,304,322,345,357,368,374,3

status

open

evidence

formal

oeis

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