A327161 - OEIS

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).

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

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.

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 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:

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