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A110176 Least k such that sigma(n)=sigma(k)+sigma(n-k) for 0<k<n, or 0 if there is no k, where sigma is the sum of divisors function. 2
0, 0, 1, 0, 0, 0, 0, 2, 4, 2, 0, 0, 0, 0, 5, 0, 0, 0, 0, 2, 7, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 4, 11, 0, 0, 0, 0, 0, 13, 10, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 17, 0, 0, 0, 12, 14, 19, 0, 0, 0, 0, 17, 19, 0, 0, 0, 0, 0, 14, 14, 0, 0, 0, 0, 25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 38, 0, 22, 22, 0, 18, 0, 30, 31, 19, 0, 12 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

Sequence A110177 gives the number of solutions 0<k<n. Note that a(n)=0 for all primes except 3. It is also zero for the composite numbers in A110178.

LINKS

Table of n, a(n) for n=1..96.

MATHEMATICA

a[n_] := Select[Range[n-1], DivisorSigma[1, n]==DivisorSigma[1, n-# ]+DivisorSigma[1, # ]&]; Table[s=a[n]; If[Length[s]==0, 0, First[s]], {n, 150}]

CROSSREFS

Cf. A066435 (least k such that sigma(n)+sigma(k)=sigma(n+k)).

Sequence in context: A009417 A009451 A321330 * A278886 A278887 A011168

Adjacent sequences:  A110173 A110174 A110175 * A110177 A110178 A110179

KEYWORD

nonn

AUTHOR

T. D. Noe, Jul 15 2005

STATUS

approved

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Last modified July 21 22:02 EDT 2019. Contains 325210 sequences. (Running on oeis4.)