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A326189
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Number of distinct nonnegative integers that are reachable from n with some nonempty combination of transitions x -> A032742(x) and x -> A302042(x).
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8
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0, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 1, 2, 2, 4, 1, 3, 1, 3, 4, 2, 1, 4, 2, 2, 4, 3, 1, 3, 1, 5, 4, 2, 2, 4, 1, 2, 3, 4, 1, 5, 1, 3, 7, 2, 1, 5, 2, 3, 4, 3, 1, 5, 4, 4, 6, 2, 1, 4, 1, 2, 6, 6, 3, 5, 1, 3, 6, 3, 1, 5, 1, 2, 4, 3, 2, 4, 1, 5, 8, 2, 1, 6, 4, 2, 4, 4, 1, 8, 4, 3, 9, 2, 3, 6, 1, 3, 6, 4, 1, 5, 1, 4, 7
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OFFSET
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1,4
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COMMENTS
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Number of distinct numbers > 1 in the directed acyclic graph formed by edge relations x -> A032742(x) and x -> A302042(x), where n is the unique root of the graph.
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LINKS
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FORMULA
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a(p) = 1 for all primes p.
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EXAMPLE
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The directed acyclic graph whose unique root is 153 (illustrated below), spans the following seven numbers [1, 5, 17, 25, 51, 75, 153], as A032742(153) = 51, A302042(153) = 75, A032742(51) = 17, A302042(51) = 25, A032742(75) = 25, A302042(75) = 15, A032742(25) = A302042(25) = 5, and A032742(17) = A302042(17) = A032742(5) = A302042(5) = 1. We exclude the root 153 from the count of numbers that are reached, thus a(153) = 6. (Equally, we can include 153, but exclude 1).
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153
/ \
/ \
51 75
/ \ / \
/ 17 \
\ | /
\ 1 /
\ /
\ /
25
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5
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1
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PROG
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(PARI)
up_to = 65537;
ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om, invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om, invec[i], (1+pt))); outvec; };
A020639(n) = if(n>1, if(n>n=factor(n, 0)[1, 1], n, factor(n)[1, 1]), 1); \\ From A020639
v078898 = ordinal_transform(vector(up_to, n, A020639(n)));
A326189aux(n, distvals) = if(1==n, distvals, my(newdistvals=setunion([n], distvals), a=A032742(n), b=A302042(n)); newdistvals = A326189aux(a, newdistvals); if(a==b, newdistvals, A326189aux(b, newdistvals)));
A326189(n) = length(A326189aux(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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