A159586 a(n) is the smallest number not yet used such that n*a(n) is a square, but n != a(n).

4, 8, 12, 1, 20, 24, 28, 2, 16, 40, 44, 3, 52, 56, 60, 9, 68, 32, 76, 5, 84, 88, 92, 6, 36, 104, 48, 7, 116, 120, 124, 18, 132, 136, 140, 25, 148, 152, 156, 10, 164, 168, 172, 11, 80, 184, 188, 27, 64, 72, 204, 13, 212, 96, 220, 14, 228, 232, 236, 15, 244, 248, 112, 49

Offset: 1

Author

Franklin T. Adams-Watters, Apr 16 2009

Keywords

• nonn

Comments

This is a self-inverse permutation of the positive integers.

Equivalently, the geometric mean of n and a(n) is an integer.

If n is squarefree, a(n) = 4n.

Crossrefs

Cf. A159253, A056135.

Programs

PARI

invect(v,n,x)=for(i=1,n,if(v[i]==x,return(1)));0
nextnew(v,n)=local(k);k=1;while(!R(n,k)||invect(v,n-1,k),k++);k
newvect(n)=local(v);v=vector(n);for(k=1,n,v[k]=nextnew(v,k));v
R(n,m)=issquare(n*m)&&n!=m
newvect(80)