

A110176


Least k such that sigma(n)=sigma(k)+sigma(nk) 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
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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[n1], 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



