Search: id:A076479
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%I A076479
%S A076479 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%T A076479 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%U A076479 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%V A076479 1,-1,-1,-1,-1,1,-1,-1,-1,1,-1,1,-1,1,1,-1,-1,1,-1,1,1,1,-1,1,-1,1,-1,
               1,-1,-1,-1,-1,1,
%W A076479 1,1,1,-1,1,1,1,-1,-1,-1,1,1,1,-1,1,-1,1,1,1,-1,1,1,1,1,1,-1,-1,-1,1,1,
               -1,1,-1,-1,1,1,
%X A076479 -1,-1,1,-1,1,1,1,1,-1,-1,1,-1,1,-1,-1,1,1,1
%N A076479 mu(sfk(n)), where mu is the Moebius-function (A008683) and sfk is the 
               square-free kernel (A007947).
%C A076479 a(n)=A008683(A007947(n)).
%C A076479 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]
%C A076479 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]
%F A076479 a(n) = (-1)^A001221(n). Multiplicative with a(p^e) = -1. - Vladeta Jovovic 
               (vladeta(AT)eunet.rs), Dec 03 2002
%Y A076479 Cf. A076480.
%Y A076479 Cf. A008836.
%Y A076479 Sequence in context: A143621 A098417 A143622 this_sequence A155040 A033999 
               A057077
%Y A076479 Adjacent sequences: A076476 A076477 A076478 this_sequence A076480 A076481 
               A076482
%K A076479 sign,mult
%O A076479 1,1
%A A076479 Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 14 2002

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