A093893 Numbers n such that every sum of two or more divisors is composite.

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

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: A318871 A330225 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