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Search: id:A008966
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| A008966 |
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1 if n is square-free, else 0. |
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+0
27
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| 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0
(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) depends only on prime signature of n (cf. A025487). So a(24) = a(375) since 24=2^3*3 and 375=3*5^3 both have prime signature (3,1).
An infinite lower triangular matrix with A008966 in the main diagonal and the rest zeros = the square of triangle A143255 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 02 2008]
a(n) = 1 - A107078(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 03 2008]
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LINKS
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Daniel Forgues, Table of n, a(n) for n=1..100000
Index entries for characteristic functions
Eric Weisstein's World of Mathematics, Moebius Function
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FORMULA
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Dirichlet g.f. zeta(s)/zeta(2s).
a(n) = abs(mu(n)), where mu is the Moebius function (A008683).
a(n) = 0^(bigomega(n)-omega(n)), where bigomega(n) and omega(n) are the numbers of prime factors of n with and without repetition (A001222, A001221, A046660). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 05 2003
Multiplicative with p^e -> 0^(e-1), p prime and e>0. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 15 2003
a(n) = 0^(A046951(n)-1). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 20 2007
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PROGRAM
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(MuPAD) func(abs(numlib::moebius(n)), n):
(MAGMA) [ Abs(MoebiusMu(n)) : n in [1..100]];
(PARI) a(n)=if(n<1, 0, direuler(p=2, n, 1+X))[n]
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CROSSREFS
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Cf. A008683, A008836.
Sequence in context: A130047 A157657 A008683 this_sequence A080323 A069158 A133639
Adjacent sequences: A008963 A008964 A008965 this_sequence A008967 A008968 A008969
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KEYWORD
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easy,nonn,mult
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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