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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 (list; graph; refs; listen; history; text; internal format)
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 * A307089 A239132 A307311

Adjacent sequences:  A228729 A228730 A228731 * A228733 A228734 A228735

KEYWORD

nonn,mult

AUTHOR

Emeric Deutsch and Reinhard Zumkeller, Sep 01 2013

STATUS

approved

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Last modified October 14 15:03 EDT 2019. Contains 328019 sequences. (Running on oeis4.)