

A097010


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


7



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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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


MAPLE

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 * A132999 A054027 A272978
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



