

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
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OFFSET

1,2


COMMENTS

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 mufunction. (End)


LINKS



FORMULA

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



CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



