A259366 Numbers for which the differences between consecutive divisors (ordered by size) are not distinct.

6, 12, 15, 18, 20, 24, 30, 36, 40, 42, 45, 48, 54, 56, 60, 63, 66, 70, 72, 75, 78, 80, 84, 90, 91, 96, 99, 100, 102, 105, 108, 110, 112, 114, 120, 126, 130, 132, 135, 138, 140, 144, 150, 156, 160, 162, 165, 168, 174, 180, 182, 186, 189, 192, 195, 198, 200

Offset: 1

Author

Reinhard Zumkeller, Jun 25 2015

Keywords

• nonn

Examples

			.    n |  A193829(n,*)      |  A027750(n,*)         |
.  ----+--------------------+-----------------------+------------
.   10 |  {1,3,5}           |  {1,2,5,10}           |
.   11 |  {10}              |  {1,11}               |
.   12 |  {1,1,1,2,6}       |  {1,2,3,4,6,12}       |  a(2) = 12
.   13 |  {12}              |  {1,13}               |
.   14 |  {1,5,7}           |  {1,2,7,14}           |
.   15 |  {2,2,10}          |  {1,3,5,15}           |  a(3) = 15
.   16 |  {1,2,4,8}         |  {1,2,4,8,16}         |
.   17 |  {16}              |  {1,17}               |
.   18 |  {1,1,3,3,9}       |  {1,2,3,6,9,18}       |  a(4) = 18
.   19 |  {18}              |  {1,19}               |
.   20 |  {1,2,1,5,10}      |  {1,2,4,5,10,20}      |  a(5) = 20
.   21 |  {2,4,14}          |  {1,3,7,21}           |
.   22 |  {1,9,11}          |  {1,2,11,22}          |
.   23 |  {22}              |  {1,23}               |
.   24 |  {1,1,1,2,2,4,12}  |  {1,2,3,4,6,8,12,24}  |  a(6) = 24
.   25 |  {4,20}            |  {1,5,25}             |            .
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A193829, A027750, A060682, A000005, A060683 (complement), subsequence of A129512.

Programs

Haskell

a259366 n = a259366_list !! (n-1)
a259366_list = filter (\x -> a060682 x < a000005' x - 1) [2..]

Mathematica

q[k_] := Module[{d = Differences[Divisors[k]]}, CountDistinct[d] < Length[d]]; Select[Range[200], q] (* Amiram Eldar, Jan 27 2025 *)

Formula

A060682(a(n)) < A000005(a(n)) - 1.