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%I #10 Jan 13 2020 09:34:26
%S 30,40,54,350,380,414,500,532,544,558,608,620,644,666,726,740,1372,
%T 2002,2190,2368,2370,2490,2624,2670,2910,3030,3090,3162,3210,3250,
%U 3270,3390,3410,3430,3810,3880,3930,4040,4110,4120,4170,4280,4360,4470,4520,4530
%N Numbers k such that exactly three subsets of proper divisors of k sum to k.
%C Or numbers k such that A065205(k) = 3.
%H Amiram Eldar, <a href="/A152616/b152616.txt">Table of n, a(n) for n = 1..1000</a>
%e The proper divisors of 30 = {1,2,3,5,6,10,15} and 30 = 5+10+15 = 2+3+10+15 = 1+3+5+6+15.
%t seqQ[n_] := Module[{d = Most[Divisors[n]]}, SeriesCoefficient[Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, n}], n] == 3]; Select[Range[1000], seqQ[#] &] (* _Amiram Eldar_, Jan 13 2020 *)
%Y Cf. A064771, A065205, A065235, A152615.
%K nonn
%O 1,1
%A _Zak Seidov_, Oct 29 2009
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