cp's OEIS Frontend

A327161 Number of positive integers that are reachable from n with some combination of transitions x -> usigma(x)-x and x -> gcd(x,phi(x)), where usigma is the sum of unitary divisors of n (A034448), and phi is Euler totient function (A000010).

%I A327161 #19 Sep 10 2019 21:51:53
%S A327161 1,2,2,3,2,3,2,4,3,5,2,5,2,6,4,5,2,7,2,6,4,7,2,6,3,6,4,6,2,10,2,6,5,7,
%T A327161 3,8,2,8,4,7,2,10,2,6,5,7,2,8,3,8,5,8,2,10,4,6,4,7,2,4,2,8,5,7,3,6,2,
%U A327161 8,5,9,2,9,2,8,4,7,3,5,2,9,5,7,2,8,3,8,6,7,2,4,5,7,5,9,4,11,2,11,5,13,2,10,2,8,7
%N A327161 Number of positive integers that are reachable from n with some combination of transitions x -> usigma(x)-x and x -> gcd(x,phi(x)), where usigma is the sum of unitary divisors of n (A034448), and phi is Euler totient function (A000010).
%C A327161 Question: Is this sequence well-defined for every n > 0? If A318882 is not well-defined for all positive integers, then neither can this be.
%H A327161 Antti Karttunen, <a href="/A327161/b327161.txt">Table of n, a(n) for n = 1..20000</a>
%H A327161 Antti Karttunen, <a href="/A327161/a327161.txt">Data supplement: n, a(n) computed for n = 1..100000</a>
%F A327161 a(n) >= max(A318882(n), 1+A326195(n)).
%e A327161 a(30) = 10 as the graph obtained from vertex-relations x -> A034460(x) and x -> A009195(x) spans the following ten numbers [1, 2, 4, 6, 8, 12, 18, 30, 42, 54], which is illustrated below:
%e A327161 .
%e A327161   30 -> 42 -> 54 (-> 30 ...)
%e A327161    |     |     |
%e A327161    2 <-- 6 <- 18
%e A327161    |  \        |
%e A327161    1 <-- 4 <- 12
%e A327161             \  |
%e A327161              <-8
%o A327161 (PARI)
%o A327161 A034460(n) = (sumdivmult(n, d, if(gcd(d, n/d)==1, d))-n); \\ From A034460
%o A327161 A327161aux(n,xs) = if(vecsearch(xs,n),xs, xs = setunion([n],xs); if(1==n,xs, my(a=A034460(n), b=gcd(eulerphi(n),n)); xs = A327161aux(a,xs); if((a==b),xs, A327161aux(b,xs))));
%o A327161 A327161(n) = length(A327161aux(n,Set([])));
%Y A327161 Cf. A000010, A009195, A034448, A034460, A318882, A326195.
%Y A327161 Cf. also A326196, A326198, A327160.
%K A327161 nonn
%O A327161 1,2
%A A327161 _Antti Karttunen_, Aug 25 2019