A124330 a(n)= ((d(n) mod phi(n)) +1)th positive integer which is coprime to n, where phi(n) is number of positive integers which are <= n and are coprime to n and d(n) is the number of positive divisors of n.

1, 1, 1, 3, 3, 1, 3, 1, 5, 1, 3, 7, 3, 11, 8, 11, 3, 1, 3, 17, 8, 9, 3, 1, 4, 9, 7, 15, 3, 1, 3, 13, 7, 9, 6, 29, 3, 9, 7, 21, 3, 29, 3, 15, 13, 9, 3, 31, 4, 17, 7, 15, 3, 25, 6, 19, 7, 9, 3, 47, 3, 9, 11, 15, 6, 29, 3, 13, 7, 27, 3, 37, 3, 9, 13, 13, 5, 29, 3, 27, 8, 9, 3, 43, 6, 9, 7, 19, 3, 47, 5

Offset: 1

Author

Leroy Quet and Ray Chandler, Oct 26 2006

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A000005, A000010, A124218, A124331.

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

A124330(n) = { my(k=1+(numdiv(n)%eulerphi(n))); for(i=1,oo,if(1==gcd(i,n),k--;if(!k,return(i)))); }; \\ Antti Karttunen, Feb 18 2023