A091011 Numbers having at least one divisor, d, such that for some x, d-x and d+x are also divisors.

6, 12, 15, 18, 24, 28, 30, 36, 40, 42, 45, 48, 54, 56, 60, 66, 72, 75, 78, 80, 84, 90, 91, 96, 102, 105, 108, 112, 114, 120, 126, 132, 135, 138, 140, 144, 150, 153, 156, 160, 162, 165, 168, 174, 180, 182, 186, 190, 192, 195, 196, 198, 200, 204, 210, 216, 220

Offset: 1

Author

Reinhard Zumkeller, Dec 13 2003

Keywords

• nonn

Comments

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

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

Crossrefs

Cf. A091009, A091010, A337331.

Programs

Mathematica

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 *)