A158387 - OEIS

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A158387

Sign of parity of number of divisors of n.

-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; internal format)

	OFFSET	`1,1`
	COMMENTS	`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).`
	LINKS	`Index to divisibility sequences`
	EXAMPLE	`a(12) = (-1)^6 = 1.`
	CROSSREFS	`Cf. A000005.` `Sequence in context: A157895 A063747 A077008 * A008836 A087960 A164660` `Adjacent sequences: A158384 A158385 A158386 * A158388 A158389 A158390`
	KEYWORD	`sign`
	AUTHOR	`Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Mar 17 2009`

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Last modified February 17 19:13 EST 2012. Contains 206085 sequences.