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

1,1

Links

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

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A129510, A066446, A129511 (complement).

Subsequences: A008588, A008597, A129521, A259366.

Sequence in context: A005279 A343281 A375611 * A259366 A196391 A343207

Adjacent sequences: A129509 A129510 A129511 * A129513 A129514 A129515

Keyword

nonn

Author

Reinhard Zumkeller, Apr 19 2007

Status

approved