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A228732
Number of independent subsets in the rooted tree with Matula-Goebel number n that do not contain the root.
3
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
OFFSET
1,2
COMMENTS
A184165(n) = A228731(n) + a(n);
this sequence and A228731 are defined by a pair of mutually recursive functions, see A184165 for definition (called b and c there).
FORMULA
Completely multiplicative with a(prime(t)) = A228731(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][[2]];
a /@ Range[1, 80] (* Jean-François Alcover, Sep 20 2019 *)
PROG
(Haskell) see A184165.
CROSSREFS
Sequence in context: A305211 A091951 A063283 * A355810 A331173 A307089
KEYWORD
nonn,mult
AUTHOR
STATUS
approved