A209249 Even numbers that are not the sum of two untouchable numbers.

2, 6, 8, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 92, 94, 96, 100, 102, 106, 108, 110, 112, 114, 116, 118, 120, 124, 128, 130, 132, 134, 136, 138

Offset: 1

Author

Donovan Johnson, Jan 13 2013

Keywords

• nonn

Comments

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.

Examples

			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.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..118
• Eric Weisstein's World of Mathematics, Untouchable Number.
• Wikipedia, Untouchable number

Crossrefs

Cf. A005114.

Programs

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)))