A293233 a(1) = 1; and for n > 1, a(n) = mu(n) * a(floor(n/2)), where mu is the Moebius function A008683.

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, -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, -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

Offset

1

Comments

See comments and illustration in A293230.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65536

Mathematica

Fold[Append[#1, MoebiusMu[#2] #1[[Floor[#2/2]]]] &, {1}, Range[2, 105]] (* Michael De Vlieger, Oct 10 2017 *)

Prog

(Scheme, with memoization-macro definec)
(definec (A293233 n) (if (= 1 n) 1 (* (A008683 n) (A293233 (/ (- n (A000035 n)) 2)))))
;; This version just demonstrates how a(n) can be computed from A292258(n):
(define (A293233 n) (let loop ((m 1) (n (A292258 n))) (if (= 1 n) m (loop (* m (A008683 (A025487 (+ 1 (A055396 n))))) (A032742 n)))))

Crossrefs

Cf. A008683.

Cf. A293430 (gives the positions of nonzero terms), A293230 (number of nonzero terms in each range [2^n, (2^(n+1))-1]).

Cf. also A292258, A292259.

Sequence in context: A266974 A075437 A130047 * A302050 A008683 A008966

Adjacent sequences: A293230 A293231 A293232 * A293234 A293235 A293236

Keyword

sign

Author

Antti Karttunen and Michael De Vlieger, Oct 10 2017

Status

approved