A073842 a(1) = 1; for n>1, a(n) = the smallest positive integer root of n not included earlier, if such a root exists, otherwise the smallest power of n not included earlier, subject to a(n)<>n.

1, 4, 9, 2, 25, 36, 49, 64, 3, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 5, 676, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225, 6, 1369, 1444, 1521, 1600, 1681, 1764, 1849, 1936, 2025, 2116, 2209, 2304, 7, 2500, 2601, 2704

Offset

1,2

Comments

Conjectured to be a rearrangement of the natural numbers.

This is a self-inverse permutation of the positive integers, as shown by the formula. - Franklin T. Adams-Watters, Jul 31 2006

Links

Table of n, a(n) for n=1..52.

Formula

By repeatedly taking the square root, represent n in the form m^(2^k), where m is not a square and k>=0. If k is even, a(n) = m^(2^(k+1)); if k is odd, a(n) = m^(2^(k-1)). - Franklin T. Adams-Watters, Jul 31 2006

Crossrefs

Cf. A073843.

Sequence in context: A011262 A073843 A366423 * A136271 A113970 A021957

Adjacent sequences: A073839 A073840 A073841 * A073843 A073844 A073845

Keyword

nonn

Author

Amarnath Murthy, Aug 13 2002

Extensions

Extended and edited by John W. Layman, Jun 25 2003

Status

approved