A097010 Numbers n such that zero is eventually reached when the map x -> A034460(x) is iterated, starting from x = n.

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

Offset

1,2

Comments

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.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10001

Mathematica

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]

Prog

(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

Crossrefs

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 * A351227 A132999 A054027

Adjacent sequences: A097007 A097008 A097009 * A097011 A097012 A097013

Keyword

nonn

Author

Labos Elemer, Aug 31 2004

Extensions

Edited by Antti Karttunen, Sep 24 2018

Status

approved