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%I #28 Jun 12 2021 23:19:43
%S 6,12,18,20,24,28,30,36,40,42,45,48,54,56,60,63,66,70,72,78,80,84,88,
%T 90,96,99,100,102,104,105,108,110,112,114,117,120,126,130,132,135,138,
%U 140,144,150,154,156,160,162,165,168,170,174,175,176,180,182,186
%N Contracted numbers.
%C n is said to be contracted if and only if n has distinct divisors d_1 < d_2 < ... < d_k such that d_1+d_2+...+d_(k-1) >= d_k. Note that d_k need not be the greatest divisor of n -- see the examples.
%H Alois P. Heinz, <a href="/A051774/b051774.txt">Table of n, a(n) for n = 1..10000</a>
%e 6 has divisors 1, 2, 3, 6, and 1+2 >= 3, so 6 is a member. 45 has divisors 1, 3, 5, 9, 15, 45, and 1+3+5+9 = 18 > 15, so 45 is a member. - _N. J. A. Sloane_, Jun 12 2021
%t cnQ[n_]:=Module[{d=Divisors[n],len},len=Length[d];AnyTrue[Table[Take[ d,k],{k,3,len}],Total[Most[#]]>=Last[#]&]]; Select[Range[200],cnQ] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jun 12 2021 *)
%Y Numbers not in A051772.
%K nonn
%O 1,1
%A Alexander Benjamin Schwartz (QBOB(AT)aol.com), Dec 08 1999
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