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A088609
a(1) = 1, a(n) is the smallest squarefree number not included earlier if n is not squarefree, else n is the smallest nonsquarefree number.
3
1, 4, 8, 2, 9, 12, 16, 3, 5, 18, 20, 6, 24, 25, 27, 7, 28, 10, 32, 11, 36, 40, 44, 13, 14, 45, 15, 17, 48, 49, 50, 19, 52, 54, 56, 21, 60, 63, 64, 22, 68, 72, 75, 23, 26, 76, 80, 29, 30, 31, 81, 33, 84, 34, 88, 35, 90, 92, 96, 37, 98, 99, 38, 39, 100, 104, 108, 41, 112, 116
OFFSET
1,2
COMMENTS
From Antti Karttunen, Jun 04 2014: (Start)
This is a self-inverse permutation (involution) of natural numbers.
After 1, nonsquarefree numbers occur (in monotonic order) at the positions given by squarefree numbers, A005117, and squarefree numbers occur (in monotonic order) at the positions given by their complement, nonsquarefree numbers, A013929.
(End)
FORMULA
From Antti Karttunen, Jun 04 2014: (Start)
a(1), and for n>1, if mu(n) = 0, a(n) = A005117(1+A057627(n)), otherwise, a(n) = A013929(A013928(n)). [Here mu is Moebius mu-function, A008683, which is zero only when n is a nonsquarefree number, one of the numbers in A013929].
For all n > 1, A008966(a(n)) = 1 - A008966(n), or equally, mu(a(n)) + 1 = mu(n) modulo 2. [A property shared with A243347].
(End)
PROG
(define (A088609 n) (cond ((<= n 1) n) ((zero? (A008966 n)) (A005117 (+ 1 (A057627 n)))) (else (A013929 (A013928 n))))) ;; Antti Karttunen, Jun 04 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Oct 16 2003
EXTENSIONS
More terms from Ray Chandler, Oct 18 2003
STATUS
approved