1,3

The number of solutions is always even because k=n/2 cannot be a solution for even n.

Table of n, a(n) for n=1..105.

a[n_] := Select[Range[n-1], DivisorSigma[1, n]==DivisorSigma[1, n-# ]+DivisorSigma[1, # ]&]; Table[Length[a[n]], {n, 150}]

Cf. A110176 (least k such that sigma(n)=sigma(k)+sigma(n-k)).

Sequence in context: A125250 A048113 A028961 * A036273 A342563 A343633

Adjacent sequences: A110174 A110175 A110176 * A110178 A110179 A110180

nonn

T. D. Noe, Jul 15 2005

approved