Erdős problem 955 · problems.science

If $A\subset \mathbb{N}$ has density $0$ then $s^{-1}(A)$ must also have density $0$ .

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12 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

955.lean

Retained formal statement7 of 12

Troupe [Tr15] has shown that this is true if $A$ is the set of integers with unusually many prime factors.

FormalConjectures/ErdosProblems/955.leanErdos955.erdos_955.variants.troupe_unusually_many_prime_factors5 linesExact file

1∀ ε > 0,2  {x |3        (1 + ε) * Real.log (Real.log ↑(Erdos955.s x)) <4          ↑(ArithmeticFunction.cardDistinctFactors (Erdos955.s x))}.HasDensity5    0

SolvedStatement only, no proof

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