A129510
Number of distinct differences between pairs of distinct divisors of n.
Original entry on oeis.org
0, 1, 1, 3, 1, 5, 1, 6, 3, 6, 1, 10, 1, 6, 5, 10, 1, 13, 1, 13, 6, 6, 1, 18, 3, 6, 6, 14, 1, 19, 1, 15, 6, 6, 6, 24, 1, 6, 6, 22, 1, 23, 1, 15, 12, 6, 1, 30, 3, 15, 6, 15, 1, 25, 6, 23, 6, 6, 1, 37, 1, 6, 13, 21, 6, 25, 1, 15, 6, 24, 1, 40, 1, 6, 13, 15, 6, 26, 1, 34, 10, 6, 1, 45, 6, 6, 6, 26
Offset: 1
n=44, set of divisors of 44 = {1,2,4,11,22,44}:
44-22=22, 44-11=33, 44-4=40, 44-2=42, 44-1=41,
22-11=11, 22-4=18, 22-2=20, 22-1=21,
11-4=7, 11-2=9, 11-1=10, 4-2=2, 4-1=3, 2-1=1,
a(44) = #{1,2,3,7,9,10,11,18,20,21,22,33,40,41,42} = 15;
n=45, set of divisors of 45 = {1,3,5,9,15,45}:
45-15=30, 45-9=36, 45-5=40, 45-3=42, 45-1=44,
15-9=6, 15-5=10, 15-3=12, 15-1=14,
9-5=4, 9-3=6, 9-1=8, 5-3=2, 5-1=4, 3-1=2,
a(45) = #{2,4,6,8,10,12,14,30,36,40,42,44} = 12.
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a[n_]:=Length[Union[Flatten[Differences/@Subsets[Divisors[n],{2}]]]];Table[a[n],{n,88}] (* James C. McMahon, Jan 21 2025 *)
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a(n)=my(d=divisors(n),v=List()); for(i=1,#d-1,for(j=i+1,#d, listput(v,d[j]-d[i]))); #Set(v) \\ Charles R Greathouse IV, Aug 26 2015
A129511
Numbers such that all differences between distinct divisors occur exactly once.
Original entry on oeis.org
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
See example for a(33)=44 in A129510.
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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
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Select[Range[103],CountDistinct[Differences /@ Subsets[Divisors[#], {2}]]==Length[Flatten[Differences /@ Subsets[Divisors[#], {2}]]]&] (* James C. McMahon, Jan 21 2025 *)
A259366
Numbers for which the differences between consecutive divisors (ordered by size) are not distinct.
Original entry on oeis.org
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
. 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} | .
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a259366 n = a259366_list !! (n-1)
a259366_list = filter (\x -> a060682 x < a000005' x - 1) [2..]
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q[k_] := Module[{d = Differences[Divisors[k]]}, CountDistinct[d] < Length[d]]; Select[Range[200], q] (* Amiram Eldar, Jan 27 2025 *)
Showing 1-3 of 3 results.
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