A391118 - OEIS

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).

%I #32 Jan 15 2026 15:43:40

%S 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,

%T 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,

%U 10,10,10,10,12,12,12,12,10,10,10,10,11,11,12,12,12,11,12

%N 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).

%H Thomas Bloom, <a href="https://www.erdosproblems.com/693">Problem #693</a>, Erdős Problems.

%H Paul Erdős, <a href="https://www.numdam.org/item/AST_1979__61__73_0/">Some unconventional problems in number theory</a>, Astérisque no. 61 (1979), 73-82.

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

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

%K nonn

%O 3,1

%A _Elijah Beregovsky_, Dec 28 2025