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A139718 A number n is included if |k - n/k| divides n for at least one divisor k of n.

%I A139718 #13 Jun 09 2025 00:51:53
%S A139718 2,6,8,12,18,20,24,30,32,36,42,48,50,54,56,60,72,80,90,96,98,108,110,
%T A139718 120,128,132,140,144,150,156,162,168,180,182,192,200,210,216,224,240,
%U A139718 242,252,270,272,288,294,300,306,320,324,336,338,342,350,360,378,380
%N A139718 A number n is included if |k - n/k| divides n for at least one divisor k of n.
%C A139718 All terms are even. All positive integers of the form n(n+1) are included.
%H A139718 Alexis Olson, <a href="/A139718/b139718.txt">Table of n, a(n) for n = 1..526</a>
%e A139718 36 is included because 3 is a divisor of 36 and |3 - 36/3| = 9 divides 36.
%t A139718 For[n = 1; s = {}, n <= 1000, n++,
%t A139718   For[i = 1, i <= Length[Divisors[n]], i++, k = Divisors[n][[i]];
%t A139718     If[Abs[k-n/k]>0&&Mod[n, Abs[k-n/k]]==0,s=Union[s,{n}];Break[]]]];s (* Alexis Olson (AlexisOlson(AT)gmail.com), Nov 14 2008 *)
%t A139718 odkQ[n_]:=Module[{d=Divisors[n],nz},nz=#-n/#&/@d; MemberQ[Divisible[ n,Abs[Select[nz,#!=0&]]],True]]; Select[Range[400],odkQ] (* _Harvey P. Dale_, May 06 2012 *)
%Y A139718 Cf. A139719.
%K A139718 nonn
%O A139718 1,1
%A A139718 _Leroy Quet_, May 01 2008
%E A139718 More terms from Alexis Olson (AlexisOlson(AT)gmail.com), Nov 14 2008