A318880 a(n) = 0 if iteration of the map k -> A034460(k) reaches zero when started from k = n, otherwise 1, when it ends into a cycle.

0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0

Offset

1

Comments

Characteristic function of A003062.

Links

Antti Karttunen, Table of n, a(n) for n = 1..87360

Index entries for characteristic functions

Formula

a(A003062(n)) = 1, a(A097010(n)) = 0.

Mathematica

a034460[0] = 0; (* avoids dividing by 0 when an iteration reaches 0 *)
a034460[n_] := Total[Select[Divisors[n], GCD[#, n/#]==1&]]-n/; n>0
periodicB[k_] := Boole[NestWhile[a034460, k, UnsameQ, All]!=0]
a318880[n_] := Map[periodicB, Range[n]]
a318880[120] (* Hartmut F. W. Hoft, Jan 25 2024 *)

Prog

(PARI)
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))); };

Crossrefs

Cf. A003062, A034460, A097010, A097032, A097033, A318882, A318883.

Sequence in context: A011679 A011682 A185015 * A177063 A341619 A302049

Adjacent sequences: A318877 A318878 A318879 * A318881 A318882 A318883

Keyword

nonn

Author

Antti Karttunen, Sep 23 2018

Status

approved