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

Author

Emeric Deutsch and Reinhard Zumkeller, Sep 01 2013

Keywords

• nonn
• mult

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

Crossrefs

Cf. A184165, A228732.

Programs

Haskell

see A184165.

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 *)

Formula

Completely multiplicative with a(prime(t)) = A228732(t). - Andrew Howroyd, Aug 01 2018