cp's OEIS Frontend

A326198 Number of positive integers that are reachable from n with some combination of transitions x -> x-phi(x) and x -> gcd(x,phi(x)).

%I A326198 #20 Sep 10 2019 21:50:48
%S A326198 1,2,2,3,2,4,2,4,3,5,2,5,2,5,3,5,2,7,2,6,4,6,2,6,3,6,4,6,2,7,2,6,3,8,
%T A326198 3,8,2,7,5,7,2,9,2,7,5,7,2,7,3,10,3,7,2,11,5,7,5,8,2,8,2,7,5,7,3,8,2,
%U A326198 9,4,8,2,9,2,8,5,8,3,12,2,8,5,10,2,10,5,8,3,8,2,10,3,8,5,8,3,8,2,9,6,11,2,9,2,8,6
%N A326198 Number of positive integers that are reachable from n with some combination of transitions x -> x-phi(x) and x -> gcd(x,phi(x)).
%H A326198 Antti Karttunen, <a href="/A326198/b326198.txt">Table of n, a(n) for n = 1..16384</a>
%H A326198 Antti Karttunen, <a href="/A326198/a326198.txt">Data supplement: n, a(n) computed for n = 1..100000</a>
%F A326198 a(n) > max(A071575(n), A326195(n)).
%e A326198 From n = 12 we can reach any of the following numbers > 0: 12 (with an empty sequence of transitions), 8 (as A051953(12) = 8), 4 (as A009195(12) = A009195(8) = A051953(8) = 4), 2 (as A009195(4) = A051953(4) = 2) and 1 (as A009195(2) = A051953(2) = 1), thus a(12) = 5.
%e A326198 The directed acyclic graph formed from those two transitions with 12 as its unique root looks like this:
%e A326198     12
%e A326198     / \
%e A326198    |   8
%e A326198     \ /
%e A326198      4
%e A326198      |
%e A326198      2
%e A326198      |
%e A326198      1
%o A326198 (PARI)
%o A326198 A326198aux(n,xs) = if(vecsearch(xs,n),xs, xs = setunion([n],xs); if(1==n,xs, my(a=gcd(n,eulerphi(n)), b=n-eulerphi(n)); xs = A326198aux(a,xs); if((a==b),xs, A326198aux(b,xs))));
%o A326198 A326198(n) = length(A326198aux(n,Set([])));
%Y A326198 Cf. A000010, A009195, A051953, A071575, A300243, A326195.
%Y A326198 Cf. also A326189, A326196, A327160, A327161.
%K A326198 nonn
%O A326198 1,2
%A A326198 _Antti Karttunen_, Aug 24 2019