

A228731


Number of independent subsets in the rooted tree with MatulaGoebel number n that contain the root.


3



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
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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 MatulaGoebel 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] (* JeanFrançois 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



