A228732 Number of independent subsets in the rooted tree with Matula-Goebel number n that do not contain the root.

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).

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Index entries for sequences related to Matula-Goebel numbers

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

Cf. A184165, A228731.

Sequence in context: A305211 A091951 A063283 * A355810 A331173 A307089

Adjacent sequences: A228729 A228730 A228731 * A228733 A228734 A228735

Keyword

nonn,mult

Author

Emeric Deutsch and Reinhard Zumkeller, Sep 01 2013

Status

approved