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

1,1

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.

Links

Table of n, a(n) for n=1..64.

Prog

(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)

Crossrefs

Cf. A159253, A056135.

Sequence in context: A164088 A109239 A056135 * A120230 A086480 A260249

Adjacent sequences: A159583 A159584 A159585 * A159587 A159588 A159589

Keyword

nonn

Author

Franklin T. Adams-Watters, Apr 16 2009

Status

approved