A159193 a(n) is the smallest positive integer not yet in the sequence with gcd(n,a(n)) > 1 but a(n) != n; a(1) = 1 by convention.

1, 4, 6, 2, 10, 3, 14, 12, 15, 5, 22, 8, 26, 7, 9, 18, 34, 16, 38, 24, 27, 11, 46, 20, 30, 13, 21, 32, 58, 25, 62, 28, 36, 17, 40, 33, 74, 19, 42, 35, 82, 39, 86, 48, 50, 23, 94, 44, 56, 45, 54, 60, 106, 51, 65, 49, 63, 29, 118, 52, 122, 31, 57, 66, 55, 64, 134, 70, 72, 68, 142

Offset: 1

Author

Franklin T. Adams-Watters, Apr 05 2009

Keywords

• nonn

Comments

This is a permutation of the positive integers with a(a(n)) = n.

Does every positive rational occur as a value of a(n)/n?

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Programs

Mathematica

a = {1}; Do[AppendTo[a, Complement[Select[Range[Max[a] + 2 n], GCD[#, n] > 1 &], a, {n}][[1]]], {n, 2, 71}]; a (* Ivan Neretin, Jul 09 2015 *)

PARI

va(n) = local(v); v=vector(n);v[1]=1;for(k=2,n,v[k]=na(v,k));v
na(v, k) = for(i=1,2*k,if(gcd(i,k)>1&&i!=k,if(!inv(v,k-1,i),return(i))))
inv(v, k, x) = for(i=1,k,if(v[i]==x,return(1)));return(0)