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 A228731 Number of independent subsets in the rooted tree with Matula-Goebel number n that contain the root. 3
 1, 1, 2, 1, 3, 2, 4, 1, 4, 3, 5, 2, 6, 4, 6, 1, 5, 4, 8, 3, 8, 5, 9, 2, 9, 6, 8, 4, 10, 6, 8, 1, 10, 5, 12, 4, 12, 8, 12, 3, 8, 8, 10, 5, 12, 9, 15, 2, 16, 9, 10, 6, 16, 8, 15, 4, 16, 10, 9, 6, 18, 8, 16, 1, 18, 10, 9, 5, 18, 12, 20, 4, 15, 12, 18, 8, 20, 12 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS A184165(n) = a(n) + A228732(n); this sequence and A228732 are defined by a pair of mutually recursive functions, see A184165 for definition (called b and c there). LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 FORMULA Completely multiplicative with a(prime(t)) = A228732(t). - Andrew Howroyd, Aug 01 2018 MATHEMATICA r[n_] := FactorInteger[n][[1, 1]]; s[n_] := n/r[n]; A[n_] := A[n] = If[n==1, {1, 1}, If[PrimeOmega[n]==1, {A[PrimePi[n]][[2]], A[PrimePi[n]] // Total}, A[r[n]] * A[s[n]]]]; a[n_] := A[n][[1]]; a /@ Range[1, 80] (* Jean-François Alcover, Sep 20 2019 *) PROG (Haskell) see A184165. CROSSREFS Cf. A184165, A228732. Sequence in context: A056892 A136523 A319855 * A163507 A003963 A003960 Adjacent sequences:  A228728 A228729 A228730 * A228732 A228733 A228734 KEYWORD nonn,mult AUTHOR Emeric Deutsch and Reinhard Zumkeller, Sep 01 2013 STATUS approved

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Last modified May 27 18:56 EDT 2020. Contains 334664 sequences. (Running on oeis4.)