%I #11 Jan 14 2013 12:31:37
%S 2,6,8,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,
%T 56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,92,94,96,100,102,
%U 106,108,110,112,114,116,118,120,124,128,130,132,134,136,138
%N Even numbers that are not the sum of two untouchable numbers.
%C It appears that this sequence has 118 terms, the last of which is 490. All even numbers from 492 to 10^7 are the sum of two untouchable numbers.
%H Donovan Johnson, <a href="/A209249/b209249.txt">Table of n, a(n) for n = 1..118</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/UntouchableNumber.html">Untouchable Number.</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Untouchable_number">Untouchable number</a>
%e 90 is not a term because it is the sum of two untouchable numbers (2 + 88). 92 is a term because no two untouchable numbers sum to 92.
%o (PARI) mx=10000; v=vector(mx); w=vector(mx); un=vector(1212); for(i=669, 1229, v[prime(i)+1]=1); for(i=2, 24989857, al=sigma(i)-i; if(al<=mx, v[al]=1)); c=0; for(i=2, mx, if(v[i]==0, c++; un[c]=i)); for(i=1, 1212, for(j=i, 1212, s=un[i]+un[j]; if(s<=mx, w[s]=1, next(2)))); n=0; forstep(i=2, mx, 2, if(w[i]==0, n++; write("b209249.txt", n " " i)))
%Y Cf. A005114.
%K nonn
%O 1,1
%A _Donovan Johnson_, Jan 13 2013