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A093893 Numbers n such that every sum of two or more divisors is composite. 3
1, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 79, 83, 87, 89, 91, 97, 101, 103, 107, 109, 113, 121, 127, 131, 133, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 183, 191, 193, 197, 199, 211, 213, 217, 223, 227, 229, 233 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

All terms are odd and very few are composite. Every odd prime is a trivial member.

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

LINKS

Table of n, a(n) for n=1..60.

MATHEMATICA

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)

fQ[n_] := Union@ PrimeQ[Plus @@@ Subsets[ Divisors@n, {2, Infinity}]] == {False}; Select[ Range[3, 235, 2], fQ@# &] (* Robert G. Wilson v, May 25 2009 *)

CROSSREFS

Cf. A093890, A093891, A093892, A093894.

Sequence in context: A242393 A210494 A275938 * A056912 A075763 A074918

Adjacent sequences:  A093890 A093891 A093892 * A093894 A093895 A093896

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Apr 23 2004

EXTENSIONS

More terms from Adam M. Kalman (mocha(AT)clarityconnect.com), Nov 11 2004

a(1)=1 prepended by Max Alekseyev, Mar 31 2015

STATUS

approved

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Last modified May 30 08:46 EDT 2017. Contains 287302 sequences.