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 A158387 a(n) = -1 if n is a square, 1 if n is not a square. 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Equivalently, a(n) is the sign of (-1)^[parity of number of divisors of n]. LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 FORMULA a(n) = (-1)^tau(n) = (-1)^A000005(n). a(1) = -1, a(p) = 1, a(pq) = 1, a(pq...z) = 1, a(p^k) = (-1)^(k+1), for p, q, ..., z primes. EXAMPLE a(12) = (-1)^6 = 1. MATHEMATICA Array[1 - 2 Boole[OddQ@ DivisorSigma[0, #]] &, 100] (* Michael De Vlieger, Nov 03 2017 *) PROG (PARI) a(n) = (-1)^numdiv(n) \\ Michel Marcus, Jun 13 2013 (PARI) a(n)=(-1)^issquare(n) \\ Charles R Greathouse IV, Jun 13 2013 (PARI) first(n) = my(res = vector(n, i, -1)); for(i = 1, sqrtint(n), res[i^2] = 1); res \\ David A. Corneth, Nov 03 2017 CROSSREFS Cf. A000005, A010052. Cf. 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). Sequence in context: A063747 A077008 * A265643 A008836 A087960 A164660 Adjacent sequences:  A158384 A158385 A158386 * A158388 A158389 A158390 KEYWORD sign,easy AUTHOR Jaroslav Krizek, Mar 17 2009 EXTENSIONS Description corrected by David A. Corneth, Nov 03 2017 STATUS approved

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Last modified November 17 10:07 EST 2018. Contains 317275 sequences. (Running on oeis4.)