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A327160
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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,usigma(x)), where usigma is the sum of unitary divisors of n (A034448).
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3
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1, 2, 2, 2, 2, 1, 2, 2, 2, 4, 2, 4, 2, 5, 4, 2, 2, 6, 2, 5, 3, 6, 2, 5, 2, 4, 2, 5, 2, 4, 2, 2, 5, 6, 3, 6, 2, 7, 3, 6, 2, 4, 2, 4, 5, 5, 2, 7, 2, 7, 5, 8, 2, 4, 3, 4, 3, 4, 2, 1, 2, 7, 3, 2, 3, 4, 2, 7, 4, 8, 2, 7, 2, 7, 3, 6, 3, 3, 2, 7, 2, 6, 2, 7, 3, 6, 6, 7, 2, 1, 5, 6, 4, 8, 4, 9, 2, 9, 5, 9, 2, 4, 2, 7, 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 ? If A318882 is not well defined in whole N, then neither this can be.
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LINKS
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EXAMPLE
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From n = 30 we can reach any of the following strictly positive numbers: 30 (e.g., with an empty sequence of transitions), 42 (as A034460(30) = 42), 54 (as A034460(42) = 54; note that A034460(54) = 30 again) and 6 as A323166(30) = A323166(42) = A323166(54) = 6 = A323166(6) = A034460(6), thus a(30) = 4.
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PROG
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(PARI)
A034448(n) = { my(f=factorint(n)); prod(k=1, #f~, 1+(f[k, 1]^f[k, 2])); }; \\ After code in A034448
A327160aux(n, xs) = if(vecsearch(xs, n), xs, xs = setunion([n], xs); if(1==n, xs, my(a=A034448(n)-n, b=gcd(A034448(n), n)); xs = A327160aux(a, xs); if((a==b), xs, A327160aux(b, xs))));
A327160(n) = length(A327160aux(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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