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%I #14 Oct 18 2017 20:37:10
%S 1,-1,-1,0,1,-1,1,0,0,1,-1,0,1,1,1,0,0,0,0,0,1,-1,1,0,0,1,0,0,-1,-1,
%T -1,0,0,0,0,0,0,0,0,0,0,-1,-1,0,0,1,-1,0,0,0,0,0,-1,0,0,0,0,-1,1,0,1,
%U -1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,0,0,0,0,0,1,-1,-1,0,0,0,0,0,0,0,0,0,0
%N a(1) = 1; and for n > 1, a(n) = mu(n) * a(floor(n/2)), where mu is the Moebius function A008683.
%C See comments and illustration in A293230.
%H Antti Karttunen, <a href="/A293233/b293233.txt">Table of n, a(n) for n = 1..65536</a>
%t Fold[Append[#1, MoebiusMu[#2] #1[[Floor[#2/2]]]] &, {1}, Range[2, 105]] (* _Michael De Vlieger_, Oct 10 2017 *)
%o (Scheme, with memoization-macro definec)
%o (definec (A293233 n) (if (= 1 n) 1 (* (A008683 n) (A293233 (/ (- n (A000035 n)) 2)))))
%o ;; This version just demonstrates how a(n) can be computed from A292258(n):
%o (define (A293233 n) (let loop ((m 1) (n (A292258 n))) (if (= 1 n) m (loop (* m (A008683 (A025487 (+ 1 (A055396 n))))) (A032742 n)))))
%Y Cf. A008683.
%Y Cf. A293430 (gives the positions of nonzero terms), A293230 (number of nonzero terms in each range [2^n, (2^(n+1))-1]).
%Y Cf. also A292258, A292259.
%K sign
%O 1
%A _Antti Karttunen_ and _Michael De Vlieger_, Oct 10 2017
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