

A228732


Number of independent subsets in the rooted tree with MatulaGoebel 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
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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 MatulaGoebel 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] (* JeanFrançois Alcover, Sep 20 2019 *)


PROG

(Haskell) see A184165.


CROSSREFS

Cf. A184165, A228731.
Sequence in context: A305211 A091951 A063283 * A331173 A307089 A239132
Adjacent sequences: A228729 A228730 A228731 * A228733 A228734 A228735


KEYWORD

nonn,mult


AUTHOR

Emeric Deutsch and Reinhard Zumkeller, Sep 01 2013


STATUS

approved



