A391118 Let B_n = {b_1 < b_2 < ...} be the set of those integers in [n, n^2] which have a divisor in (n, 2n). a(n) = max(b_(i+1) - b_i).

3, 3, 3, 3, 4, 4, 4, 4, 5, 6, 6, 5, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 9, 9, 10, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 12, 12, 12, 12, 10, 10, 10, 10, 11, 11, 12, 12, 12, 11, 12

Offset

3,1

Links

Table of n, a(n) for n=3..83.

Thomas Bloom, Problem #693, Erdős Problems.

Paul Erdős, Some unconventional problems in number theory, Astérisque no. 61 (1979), 73-82.

Formula

Conjecture of Erdős: a(n) <= (log(n))^O(1).

Mathematica

a[n_]:=Max[Differences[Select[Range[n, n^2], IntersectingQ[Divisors[#], Range[n+1, 2n-1]]&]]]

Crossrefs

Sequence in context: A309555 A262994 A179847 * A035936 A006671 A394294

Adjacent sequences: A391115 A391116 A391117 * A391119 A391120 A391121

Keyword

nonn

Author

Elijah Beregovsky, Dec 28 2025

Status

approved