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Erdős problem 887

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Is there an absolute constant KK such that, for every C>0C > 0, if nn is sufficiently large then nn has at most KK divisors in (n12,n12+Cn14)(n^{\frac{1}{2}}, n^{\frac{1}{2}} + C n^{\frac{1}{4}}).

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4 retained statements36c6d0fef71a

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FormalConjectures/ErdosProblems/

887.lean

Retained formal statement4 of 4

A question of Erdős and Rosenfeld, who proved that there are infinitely many nn with (at least) 44 divisors in (n12,n12+cn14)(n^{\frac{1}{2}}, n^{\frac{1}{2}} + cn^{\frac{1}{4}}).

FormalConjectures/ErdosProblems/887.leanErdos887.erdos_887.variants.rosenfeld_infinite1 lineExact file
∃ C > 0, Infinite ↑{n | 4 ≤ {d ∈ Finset.Ioo ⌊√↑n⌋₊ ⌈√↑n + C * ↑n ^ (1 / 4)⌉₊ | d ∣ n}.card}
SolvedStatement only, no proof