A129512 Numbers with at least two pairs of distinct divisors having equal differences.

6, 12, 15, 18, 20, 24, 28, 30, 36, 40, 42, 45, 48, 54, 56, 60, 63, 66, 70, 72, 75, 78, 80, 84, 88, 90, 91, 96, 99, 100, 102, 105, 108, 110, 112, 114, 120, 126, 130, 132, 135, 138, 140, 144, 150, 153, 156, 160, 162, 165, 168, 174, 176, 180, 182, 186, 189, 190, 192, 195

Offset: 1

Author

Reinhard Zumkeller, Apr 19 2007

Keywords

• nonn

Examples

			See example for a(12) = 45 in A129510.
		

Links

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

Crossrefs

Cf. A129510, A066446, A129511 (complement).

Subsequences: A008588, A008597, A129521, A259366.

Programs

Haskell

import Data.List.Ordered (minus)
a129512 n = a129512_list !! (n-1)
a129512_list = minus [1..] a129511_list
-- Reinhard Zumkeller, Aug 10 2015

Mathematica

q[k_] := Count[Tally[Differences /@ Subsets[Divisors[k], {2}] // Flatten][[;; , 2]], ?(# > 1 &)] > 0; Select[Range[200], q] (* _Amiram Eldar, Jan 27 2025 *)

PARI

is(n)=my(d=divisors(n)); for(i=1,#d-2, for(j=i+1,#d-1, for(k=1,#d, if(i!=k && setsearch(d, d[j]-d[i]+d[k]), return(1))))); 0 \\ Charles R Greathouse IV, Aug 26 2015

Formula

A129510(a(n)) < A066446(a(n)).