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Search: id:A076479
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| A076479 |
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mu(sfk(n)), where mu is the Moebius-function (A008683) and sfk is the square-free kernel (A007947). |
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5
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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a(n)=A008683(A007947(n)).
a(1) = 1, a(n) for n >=2 is sign of parity of number of distinct primes dividing n. a(p) = -1, a(pq) = 1, a(pq...z) = (-1)^k, a(p^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). [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Mar 17 2009]
a(n) is the unitary Moebius function, i.e., the inverse of the constant 1 function under the unitary convolution defined by (f X g)(n)= sum of f(d)g(n/d), where the sum is over the unitary divisors d of n (divisors d of n such that gcd(d,n/d)=1). [From Laszlo Toth (ltoth(AT)gamma.ttk.pte.hu), Oct 08 2009]
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FORMULA
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a(n) = (-1)^A001221(n). Multiplicative with a(p^e) = -1. - Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 03 2002
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CROSSREFS
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Cf. A076480.
Cf. A008836.
Sequence in context: A143621 A098417 A143622 this_sequence A155040 A033999 A057077
Adjacent sequences: A076476 A076477 A076478 this_sequence A076480 A076481 A076482
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KEYWORD
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sign,mult
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 14 2002
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