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A327161
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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).
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3
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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
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1,2
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COMMENTS
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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.
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LINKS
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Antti Karttunen, Table of n, a(n) for n = 1..20000
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000
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FORMULA
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a(n) >= max(A318882(n), 1+A326195(n)).
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EXAMPLE
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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:
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30 -> 42 -> 54 (-> 30 ...)
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2 <-- 6 <- 18
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1 <-- 4 <- 12
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<-8
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PROG
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(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([])));
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen, Aug 25 2019
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STATUS
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approved
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