%I #8 Feb 01 2021 18:18:14

%S 6,12,15,18,24,28,30,36,40,42,45,48,54,56,60,66,72,75,78,80,84,90,91,

%T 96,102,105,108,112,114,120,126,132,135,138,140,144,150,153,156,160,

%U 162,165,168,174,180,182,186,190,192,195,196,198,200,204,210,216,220

%N Numbers having at least one divisor, d, such that for some x, d-x and d+x are also divisors.

%C A091009(a(n)) > 0; complement of A091010.

%C Numbers k with at least one pair of divisors, (d1,d2), with d1 < d2, whose (integer) average divides k. - _Wesley Ivan Hurt_, Aug 23 2020

%t Table[If[Sum[Sum[(1 - Ceiling[(i + k)/2] + Floor[(i + k)/2]) (1 - Ceiling[2 n/(i + k)] + Floor[2 n/(i + k)]) (1 - Ceiling[n/k] + Floor[n/k]) (1 - Ceiling[n/i] + Floor[n/i]), {i, k - 1}], {k, n}] > 0, n, {}], {n, 200}] // Flatten (* _Wesley Ivan Hurt_, Aug 23 2020 *)

%Y Cf. A091009, A091010, A337331.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Dec 13 2003