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A097010
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Numbers n such that zero is eventually reached when the map x -> A034460(x) is iterated, starting from x = n.
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7
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1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 79
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refs;
listen;
history;
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OFFSET
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1,2
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COMMENTS
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Numbers n for which A318880(n) = 0. - Antti Karttunen, Sep 23 2018
The sequence doesn't contain any numbers from attractor sets like A002827, A063991, A097024, A097030, etc, nor any number x such that the iteration of the map x -> A034460(x) would lead to such an attractor set (e.g., numbers in A097034 - A097037). - Antti Karttunen, Sep 24 2018, after the original author's example.
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LINKS
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Antti Karttunen, Table of n, a(n) for n = 1..10001
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MATHEMATICA
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di[x_] :=Divisors[x]; ta={{0}}; ud[x_] :=Part[di[x], Flatten[Position[GCD[di[x], Reverse[di[x]]], 1]]]; asu[x_] :=Apply[Plus, ud[x]]-x; nsf[x_, ho_] :=NestList[asu, x, ho] Do[g=n; s=Last[NestList[asu, n, 100]]; If[Equal[s, 0], Print[{n, s}]; ta=Append[ta, n]], {n, 1, 256}]; ta = Delete[ta, 1]
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PROG
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(PARI)
up_to = 10000;
A034460(n) = (sumdivmult(n, d, if(gcd(d, n/d)==1, d))-n); \\ From A034460
A318880(n) = { my(visited = Map()); for(j=1, oo, if(mapisdefined(visited, n), return(1), mapput(visited, n, j)); n = A034460(n); if(!n, return(0))); };
A097010list(up_to) = { my(v = vector(up_to), k=0, n=1); while(k<up_to, if(!A318880(n), k++; v[k] = n); n++); (v); };
v097010 = A097010list(up_to);
A097010(n) = v097010[n]; \\ Antti Karttunen, Sep 24 2018
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CROSSREFS
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Cf. A002827, A034460, A063991, A097024, A097030, A097031, A097032, A097033, A097034, A097035, A097036, A097037.
Cf. A003062 (complement), A318880.
Differs from A129487 for the first time at n=51, as A129487(51) = 54, but that term is lacking here, as in this sequence a(51) = 55.
Sequence in context: A034153 A004725 A129487 * A132999 A054027 A272978
Adjacent sequences: A097007 A097008 A097009 * A097011 A097012 A097013
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KEYWORD
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nonn
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AUTHOR
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Labos Elemer, Aug 31 2004
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EXTENSIONS
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Edited by Antti Karttunen, Sep 24 2018
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STATUS
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approved
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