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 A166698 Totally multiplicative sequence with a(p) = a(p-1) - 1 for prime p. 1
 1, 0, -1, 0, -1, 0, -1, 0, 1, 0, -1, 0, -1, 0, 1, 0, -1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, -1, 0, -1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, -1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, 1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 FORMULA Multiplicative with a(p^e) = (a(p-1)-1)^e. If n = Product p(k)^e(k) then a(n) = Product (a(p(k)-1)-1)^e(k). Multiplicative with a(p^e) = 0 if p = 2, with a(p^e) = 1 if p > 2 and e is even, with a(p^e) = -1 if p > 2 and e is odd. a(p) = -1 for prime p > 2. a(1) = 1, for k >= 1: a(2k) = 0, a(2k - 1) = 1 if A001222(2k - 1) is even, a(2k - 1) = -1 if A001222(2k - 1) is odd, where A001222(n) = bigomega(n). Sum_{d|n} a(d) * A000012(d) = Sum_{d|n} a(d) * A000012(d/n) = A053866(n) = A093709(n) for n>= 1. a(n) = A000035(n) * A008836(n). - Antti Karttunen, Sep 14 2017 PROG (Scheme, with memoization-macro) (definec (A166698 n) (if (= 1 n) n (* (+ -1 (A166698 (+ -1 (A020639 n)))) (A166698 (A032742 n))))) ;; Antti Karttunen, Sep 14 2017 CROSSREFS Cf. A000035 (gives the absolute values), A001222, A008836. Sequence in context: A056594 A101455 A091337 * A250299 A193497 A260390 Adjacent sequences:  A166695 A166696 A166697 * A166699 A166700 A166701 KEYWORD sign,mult AUTHOR Jaroslav Krizek, Oct 18 2009 EXTENSIONS More terms from Antti Karttunen, Sep 14 2017 STATUS approved

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Last modified December 6 21:48 EST 2019. Contains 329809 sequences. (Running on oeis4.)