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A326198
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Number of positive integers that are reachable from n with some combination of transitions x -> x-phi(x) and x -> gcd(x,phi(x)).
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4
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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, 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, 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
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OFFSET
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1,2
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LINKS
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FORMULA
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EXAMPLE
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The directed acyclic graph formed from those two transitions with 12 as its unique root looks like this:
12
/ \
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\ /
4
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2
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1
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PROG
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(PARI)
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))));
A326198(n) = length(A326198aux(n, Set([])));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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