

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).


3



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, 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, 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
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OFFSET

1,2


COMMENTS

Question: Is this sequence welldefined for every n > 0? If A318882 is not welldefined for all positive integers, then neither can this be.


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..20000
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000


FORMULA

a(n) >= max(A318882(n), 1+A326195(n)).


EXAMPLE

a(30) = 10 as the graph obtained from vertexrelations 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:
.
30 > 42 > 54 (> 30 ...)
  
2 < 6 < 18
 \ 
1 < 4 < 12
\ 
<8


PROG

(PARI)
A034460(n) = (sumdivmult(n, d, if(gcd(d, n/d)==1, d))n); \\ From A034460
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))));
A327161(n) = length(A327161aux(n, Set([])));


CROSSREFS

Cf. A000010, A009195, A034448, A034460, A318882, A326195.
Cf. also A326196, A326198, A327160.
Sequence in context: A060741 A125747 A060129 * A350067 A308450 A229123
Adjacent sequences: A327158 A327159 A327160 * A327162 A327163 A327164


KEYWORD

nonn


AUTHOR

Antti Karttunen, Aug 25 2019


STATUS

approved



