%I #25 Nov 11 2023 10:39:30

%S 1,2,3,4,5,7,8,9,10,11,13,14,16,17,19,21,22,23,25,26,27,28,29,31,32,

%T 33,34,35,37,38,39,41,43,44,46,47,49,50,51,52,53,55,57,58,59,61,62,64,

%U 65,67,68,69,71,73,74,76,77,79,81,82,83,85,86,87,88,89,92,93,94,95,97,98

%N Numbers for which the differences between consecutive divisors (ordered by size) are distinct.

%C A060682(a(n)) = A000005(a(n)) - 1, n > 1. - _Reinhard Zumkeller_, Jun 25 2015

%H Reinhard Zumkeller, <a href="/A060683/b060683.txt">Table of n, a(n) for n = 1..10000</a>

%H A. Balog, P. Erdős, and G. Tenenbaum, <a href="http://dx.doi.org/10.1007/978-1-4612-3464-7_6">On Arithmetic Functions Involving Consecutive Divisors</a>, In: Analytical Number Theory, pp. 77-90, Birkhäuser, Basel, 1990.

%e For n=6, divisors={1,2,3,6}; differences={1,1,3}, which are not distinct, so 6 is not in the sequence.

%t test[n_ ] := Length[dd=Drop[d=Divisors[n], 1]-Drop[d, -1]]==Length[Union[dd]]; Select[Range[1, 100], test]

%o (Haskell)

%o a060683 n = a060683_list !! (n-1)

%o a060683_list = 1 : filter (\x -> a060682 x == a000005' x - 1) [2..]

%o -- _Reinhard Zumkeller_, Jun 25 2015

%o (PARI) isok(k) = my(d=divisors(k)); #Set(vector(#d-1, k, d[k+1]-d[k])) == #d-1; \\ _Michel Marcus_, Nov 11 2023

%Y Cf. A000005, A060680, A060681, A060682, A060765.

%Y Cf. A060682, A259366 (complement).

%K nonn

%O 1,2

%A _Labos Elemer_, Apr 19 2001

%E Edited by _Dean Hickerson_, Jan 22 2002