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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. 5
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 (list; graph; refs; listen; history; text; internal format)
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
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.
Sequence in context: A144926 A153016 A231549 * A026185 A026209 A198473
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Oct 16 2003
EXTENSIONS
More terms from Ray Chandler, Oct 18 2003
STATUS
approved

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Last modified July 20 20:50 EDT 2024. Contains 374459 sequences. (Running on oeis4.)