A110178 - OEIS

%I #3 Mar 30 2012 17:22:40

%S 4,6,12,14,16,18,22,24,25,26,27,28,34,35,36,38,42,44,45,46,48,50,52,

%T 54,58,60,64,65,66,68,72,74,76,77,78,80,81,82,84,86,91,95,98,100,102,

%U 106,112,115,118,119,120,121,122,124,132,133,138,142,143,144,146,148,154

%N Composite numbers n such that the equation sigma(n)=sigma(k)+sigma(n-k) has no solution, where sigma is the sum of divisors function.

%C The only prime for which this equation has a solution is 3.

%t a[n_] := Select[Range[n-1], DivisorSigma[1, n]==DivisorSigma[1, n-# ]+DivisorSigma[1, # ]&]; t=Table[Length[a[n]], {n, 200}]; Complement[Flatten[Position[t, 0]], Prime[Range[PrimePi[200]]]]

%K nonn

%O 1,1

%A _T. D. Noe_, Jul 15 2005