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