Search: id:A158387
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%I A158387
%S A158387 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%T A158387 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%U A158387 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%V A158387 -1,1,1,-1,1,1,1,1,-1,1,1,1,1,1,1,-1,1,1,1,1,1,1,1,1,-1,1,1,1,1,1,1,1,
               1,
%W A158387 1,1,-1,1,1,1,1,1,1,1,1,1,1,1,1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,1,1,
               1,
%X A158387 1,1,1,1,1,1,1,1,1,1,1,1,1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1
%N A158387 a(n) = sign of parity of number of divisors of n.
%C A158387 a(n) = (-1)^tau(n) = (-1)^A000005. a(1) = -1, a(p) = 1, a(pq) = 1, a(pq...z) 
               = 1, a(p^k) = (-1)^(k+1), for p = primes (A000040), pq = product 
               of two distinct primes (A006881), pq...z = product of k (k > 2) distinct 
               primes p, q, ..., z (A120944), p^k = prime powers (A000961(n) for 
               n > 1), k = natural numbers (A000027).
%e A158387 a(12) = (-1)^6 = 1.
%Y A158387 Cf.: A000005, A000040, A006881, A120944, A000961, A000027.
%Y A158387 Sequence in context: A157895 A063747 A077008 this_sequence A087960 A164660 
               A114523
%Y A158387 Adjacent sequences: A158384 A158385 A158386 this_sequence A158388 A158389 
               A158390
%K A158387 sign
%O A158387 1,1
%A A158387 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Mar 17 2009

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