A110177 Number of solutions 0

0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 4, 2, 4, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 4

Offset: 1

Author

T. D. Noe, Jul 15 2005

Keywords

• nonn

Comments

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

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

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

Cf. also A110174.

Programs

Mathematica

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

PARI

A110177(n) = { my(x=sigma(n)); sum(k=1,n-1,(x == (sigma(k)+sigma(n-k)))); }; \\ Antti Karttunen, Feb 20 2023