A124218 a(n) is the m-th positive integer which is coprime to n, where phi(n) is number of positive integers which are <= n and are coprime to n, d(n) is the number of positive divisors of n and m = phi(n) if phi(n)|d(n), else m = d(n) mod phi(n).

1, 1, 2, 1, 2, 5, 2, 7, 4, 9, 2, 5, 2, 9, 7, 9, 2, 17, 2, 13, 5, 7, 2, 23, 3, 7, 5, 13, 2, 29, 2, 11, 5, 7, 4, 25, 2, 7, 5, 19, 2, 25, 2, 13, 11, 7, 2, 29, 3, 13, 5, 11, 2, 23, 4, 17, 5, 7, 2, 43, 2, 7, 10, 13, 4, 25, 2, 11, 5, 23, 2, 35, 2, 7, 11, 11, 4, 25, 2, 23, 7, 7, 2, 41, 4, 7, 5, 17, 2, 43, 4

Offset: 1

Author

Leroy Quet, Oct 19 2006

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A000005, A000010, A124219, A124330.

Programs

Mathematica

f[n_] := Block[{k = 0, m = Mod[Length[Divisors[n]], EulerPhi[n], 1]},While[m > 0,k++;While[GCD[n, k] > 1, k++ ];m--;];k];Table[f[n], {n, 100}] (* Ray Chandler, Oct 26 2006 *)

PARI

A124218(n) = { my(d=numdiv(n), t=eulerphi(n), m=if(!(d%t), t, (d%t))); for(k=1,oo,if(1==gcd(k,n), m--; if(!m, return(k)))); }; \\ Antti Karttunen, Mar 30 2021

Extensions

Edited and extended by Ray Chandler, Oct 26 2006