A110178 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.

4, 6, 12, 14, 16, 18, 22, 24, 25, 26, 27, 28, 34, 35, 36, 38, 42, 44, 45, 46, 48, 50, 52, 54, 58, 60, 64, 65, 66, 68, 72, 74, 76, 77, 78, 80, 81, 82, 84, 86, 91, 95, 98, 100, 102, 106, 112, 115, 118, 119, 120, 121, 122, 124, 132, 133, 138, 142, 143, 144, 146, 148, 154

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..63.

Mathematica

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]]]]

Crossrefs

Sequence in context: A350864 A175593 A163097 * A318712 A140599 A282280

Adjacent sequences: A110175 A110176 A110177 * A110179 A110180 A110181

Keyword

nonn

Author

T. D. Noe, Jul 15 2005

Status

approved