erdős #380
We call an interval 'bad' if the greatest prime factor of occurs with an exponent greater than . Let count the number of which are contained in at least one bad interval. Is it true thatwhere is the largest prime factor of ?
Worked, still open.
number theory · solved · 0 attempts
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unverified AI candidates (2)
gpt-erdos · GPT-5.2 Pro + Deep Research · unverified
As far as I can tell, this is **open**: it is Erdős–Graham’s problem (listed as **Erdős Problem #380**) asking exactly whether [ B(x)\sim B'(x):=|\\{n\le x:\ P(n)^2\mid n\\}|. ] No proof (or counterexample) is currently known. ([Erdős Problems][1])
candidate solution ↗llm-hunter · gpt pro 5.2 · unverified
1 LLM attack(s) recorded (gpt pro 5.2); unverified.
candidate solution ↗oeis
A070003 — Numbers divisible by the square of their largest prime factor.4,8,9,16,18,25,27,32,36,49,50,54,64,72,75,81,98,100,108,121,125,128,144,147,150,162,169,196,200,216,225,242,243,245,250,A387054 — Elements of A388654 that do not lie in A070003.24,48,120,168,360,528,840,960,1155,1368,1680,1683,1848,1850,2208,2210,2600,2736,2737,2808,3024,3250,3480,3720,4224,4488,A388654 — Elements of an interval of natural numbers whose product is divisible by the square of the largest prime factor.4,8,9,16,18,24,25,27,32,36,48,49,50,54,64,72,75,81,98,100,108,120,121,125,128,144,147,150,162,168,169,196,200,216,225,24A389100 — Elements of a non-singleton interval of natural numbers whose product is divisible by the square of the largest prime factor of the product.8,9,24,25,48,49,50,120,121,168,169,242,243,288,289,360,361,528,529,675,676,840,841,960,961,1155,1156,1368,1369,1444,1445
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