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

%I A259366 #19 Jan 27 2025 01:26:23
%S A259366 6,12,15,18,20,24,30,36,40,42,45,48,54,56,60,63,66,70,72,75,78,80,84,
%T A259366 90,91,96,99,100,102,105,108,110,112,114,120,126,130,132,135,138,140,
%U A259366 144,150,156,160,162,165,168,174,180,182,186,189,192,195,198,200
%N A259366 Numbers for which the differences between consecutive divisors (ordered by size) are not distinct.
%H A259366 Reinhard Zumkeller, <a href="/A259366/b259366.txt">Table of n, a(n) for n = 1..10000</a>
%F A259366 A060682(a(n)) < A000005(a(n)) - 1.
%e A259366 .    n |  A193829(n,*)      |  A027750(n,*)         |
%e A259366 .  ----+--------------------+-----------------------+------------
%e A259366 .   10 |  {1,3,5}           |  {1,2,5,10}           |
%e A259366 .   11 |  {10}              |  {1,11}               |
%e A259366 .   12 |  {1,1,1,2,6}       |  {1,2,3,4,6,12}       |  a(2) = 12
%e A259366 .   13 |  {12}              |  {1,13}               |
%e A259366 .   14 |  {1,5,7}           |  {1,2,7,14}           |
%e A259366 .   15 |  {2,2,10}          |  {1,3,5,15}           |  a(3) = 15
%e A259366 .   16 |  {1,2,4,8}         |  {1,2,4,8,16}         |
%e A259366 .   17 |  {16}              |  {1,17}               |
%e A259366 .   18 |  {1,1,3,3,9}       |  {1,2,3,6,9,18}       |  a(4) = 18
%e A259366 .   19 |  {18}              |  {1,19}               |
%e A259366 .   20 |  {1,2,1,5,10}      |  {1,2,4,5,10,20}      |  a(5) = 20
%e A259366 .   21 |  {2,4,14}          |  {1,3,7,21}           |
%e A259366 .   22 |  {1,9,11}          |  {1,2,11,22}          |
%e A259366 .   23 |  {22}              |  {1,23}               |
%e A259366 .   24 |  {1,1,1,2,2,4,12}  |  {1,2,3,4,6,8,12,24}  |  a(6) = 24
%e A259366 .   25 |  {4,20}            |  {1,5,25}             |            .
%t A259366 q[k_] := Module[{d = Differences[Divisors[k]]}, CountDistinct[d] < Length[d]]; Select[Range[200], q] (* _Amiram Eldar_, Jan 27 2025 *)
%o A259366 (Haskell)
%o A259366 a259366 n = a259366_list !! (n-1)
%o A259366 a259366_list = filter (\x -> a060682 x < a000005' x - 1) [2..]
%Y A259366 Cf. A193829,  A027750, A060682, A000005, A060683 (complement), subsequence of A129512.
%K A259366 nonn
%O A259366 1,1
%A A259366 _Reinhard Zumkeller_, Jun 25 2015