A088610 Starting with n = 1, a(n) is the smallest squarefree number not included earlier if n is odd, else n is the smallest nonsquarefree number.

1, 4, 2, 8, 3, 9, 5, 12, 6, 16, 7, 18, 10, 20, 11, 24, 13, 25, 14, 27, 15, 28, 17, 32, 19, 36, 21, 40, 22, 44, 23, 45, 26, 48, 29, 49, 30, 50, 31, 52, 33, 54, 34, 56, 35, 60, 37, 63, 38, 64, 39, 68, 41, 72, 42, 75, 43, 76, 46, 80, 47, 81, 51, 84, 53, 88, 55, 90, 57, 92, 58, 96

Offset

1,2

Comments

From Antti Karttunen, Jun 04 2014: (Start)

Squarefree (A005117) and nonsquarefree numbers (A013929) interleaved, the former at odd n and the latter at even n.

A243344 is a a "recursivized" variant of this permutation. Like this one, it also satisfies the given simple identity linking the parity of n with the Moebius mu-function. (End)

Links

Antti Karttunen, Table of n, a(n) for n = 1..8192

Index entries for sequences that are permutations of the natural numbers.

Formula

From Antti Karttunen, Jun 04 2014: (Start)

a(2n) = A013929(n), a(2n-1) = A005117(n).

For all n, A008966(a(n)) = A000035(n), or equally, mu(a(n)) = n modulo 2, where mu is Moebius mu (A008683). (End)

Mathematica

With[{max = 100}, s = Select[Range[max], SquareFreeQ]; ns = Complement[Range[max], s]; Riffle[s[[1 ;; Length[ns]]], ns]] (* Amiram Eldar, Mar 04 2024 *)

Prog

(Scheme) (define (A088610 n) (if (even? n) (A013929 (/ n 2)) (A005117 (/ (+ 1 n) 2))))

Crossrefs

Inverse: A243352.

Bisections: A005117, A013929.

Similar permutations: A075378, A073846, A237056, A072061, A094077, A167151, A088609, A243344.

Cf. A000035, A008966.

Sequence in context: A144926 A153016 A231549 * A026185 A026209 A198473

Adjacent sequences: A088607 A088608 A088609 * A088611 A088612 A088613

Keyword

nonn

Author

Amarnath Murthy, Oct 16 2003

Extensions

More terms from Ray Chandler, Oct 18 2003

Status

approved