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A110177 Number of solutions 0<k<n to the equation sigma(n)=sigma(k)+sigma(n-k), where sigma is the sum of divisors function. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

LINKS

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

MATHEMATICA

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

CROSSREFS

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

KEYWORD

nonn

AUTHOR

T. D. Noe, Jul 15 2005

STATUS

approved

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Last modified June 22 04:06 EDT 2021. Contains 345367 sequences. (Running on oeis4.)