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%I #10 Jul 25 2015 00:49:34
%S 1,3,5,7,11,13,17,19,23,29,31,37,41,43,47,49,53,59,61,67,71,73,79,83,
%T 87,89,91,97,101,103,107,109,113,121,127,131,133,137,139,149,151,157,
%U 163,167,169,173,179,181,183,191,193,197,199,211,213,217,223,227,229,233
%N Numbers n such that every sum of two or more divisors is composite.
%C All terms are odd and very few are composite. Every odd prime is a trivial member.
%C Very few terms have more than four divisors. The smallest such term is 4753, which has six divisors: 1,7,49,97,679,4753. - Adam M. Kalman (mocha(AT)clarityconnect.com), Nov 11 2004
%t For[a:=3, a<=500, s =Divisors[a];n := 1;d := False; While[(n<=2^Length[s])\[And]( ["not" character]d), If[Length[NthSubset[n, s]]>=2, If[ !PrimeQ[Plus@@NthSubset[n, s]], n++, d:= True], n++ ]]; If[ ["not" character]d, Print[a]];a+=2]; (Kalman)
%t fQ[n_] := Union@ PrimeQ[Plus @@@ Subsets[ Divisors@n, {2, Infinity}]] == {False}; Select[ Range[3, 235, 2], fQ@# &] (* _Robert G. Wilson v_, May 25 2009 *)
%Y Cf. A093890, A093891, A093892, A093894.
%K nonn
%O 1,2
%A _Amarnath Murthy_, Apr 23 2004
%E More terms from Adam M. Kalman (mocha(AT)clarityconnect.com), Nov 11 2004
%E a(1)=1 prepended by _Max Alekseyev_, Mar 31 2015
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