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

Author

Labos Elemer, Aug 31 2004

Keywords

• nonn

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

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.

Programs

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]

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(kA318880(n), k++; v[k] = n); n++); (v); };
v097010 = A097010list(up_to);
A097010(n) = v097010[n]; \\ Antti Karttunen, Sep 24 2018

Extensions

Edited by Antti Karttunen, Sep 24 2018