A129511 Numbers such that all differences between distinct divisors occur exactly once.

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 31, 32, 33, 34, 35, 37, 38, 39, 41, 43, 44, 46, 47, 49, 50, 51, 52, 53, 55, 57, 58, 59, 61, 62, 64, 65, 67, 68, 69, 71, 73, 74, 76, 77, 79, 81, 82, 83, 85, 86, 87, 89, 92, 93, 94, 95, 97, 98, 101, 103

Offset: 1

Author

Reinhard Zumkeller, Apr 19 2007

Keywords

• nonn

Comments

A129510(a(n)) = A066446(a(n)).

a(n) = A174905(n) for n<27, A174905(27)=37 whereas a(27)=35. - Reinhard Zumkeller, Apr 01 2010

Examples

			See example for a(33)=44 in A129510.
		

Links

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

Crossrefs

Cf. A027750, A066446, A129510, A129512 (complement), A174905.

Programs

Haskell

import Data.List.Ordered (isect, union)
a129511 n = a129511_list !! (n-1)
a129511_list = filter (f [] . a027750_row') [1..] where
   f  [] = True
   f zs (d:ds) = null (dds `isect` zs) && f (dds `union` zs) ds
                 where dds = map (subtract d) ds
-- Reinhard Zumkeller, Jun 25 2015

Mathematica

Select[Range[103],CountDistinct[Differences /@ Subsets[Divisors[#], {2}]]==Length[Flatten[Differences /@ Subsets[Divisors[#], {2}]]]&] (* James C. McMahon, Jan 21 2025 *)