A228731 Number of independent subsets in the rooted tree with Matula-Goebel number n that contain the root.

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

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

Index entries for sequences related to Matula-Goebel numbers

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