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A228732
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Number of independent subsets in the rooted tree with Matula-Goebel number n that do not contain the root.
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3
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1, 2, 3, 4, 5, 6, 5, 8, 9, 10, 8, 12, 8, 10, 15, 16, 9, 18, 9, 20, 15, 16, 13, 24, 25, 16, 27, 20, 13, 30, 13, 32, 24, 18, 25, 36, 14, 18, 24, 40, 14, 30, 14, 32, 45, 26, 21, 48, 25, 50, 27, 32, 17, 54, 40, 40, 27, 26, 14, 60, 22, 26, 45, 64, 40, 48, 17, 36
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OFFSET
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1,2
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COMMENTS
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this sequence and A228731 are defined by a pair of mutually recursive functions, see A184165 for definition (called b and c there).
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LINKS
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FORMULA
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MATHEMATICA
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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][[2]];
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PROG
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CROSSREFS
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KEYWORD
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nonn,mult
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AUTHOR
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STATUS
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approved
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