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A008966
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1 if n is squarefree, else 0.
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60
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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; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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]
A175046(n) = a(n)*A073311(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 05 2010]
a(A005117(n))=1; a(A013929(n))=0; a(n)=A013928(n+1)-A013928(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 05 2010]
a(n) * A112526(n) = A063524(n). [Reinhard Zumkeller, Sep 16 2011]
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LINKS
| 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
| 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
a(n)=floor(rad(n)/n), where rad(n) is A007947 [From Barbarel Tres Mil (barbarel3000(AT)yahoo.es), Nov 13 2009]
a(n)=floor(A000005(n^2)/A007425(n)) [From E. Perez Herrero (psychgeometry(AT)gmail.com), Apr 15 2010]
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MAPLE
| A008966 := proc(n) if numtheory[issqrfree](n) then 1 ; else 0 ; end if; end proc: # R. J. Mathar, Mar 14 2011
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MATHEMATICA
| A008966[n_]:=Abs[MoebiusMu[n]]; [From E. Perez Herrero (psychgeometry(AT)gmail.com), Apr 15 2010]
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PROG
| (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]
(Haskell)
a008966 n = fromEnum (n == 1 || n' `mod` spf > 0 && a008966 n' == 1)
where n' = n `div` spf
spf = a020639 n
-- Reinhard Zumkeller, Jan 25 2012
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CROSSREFS
| Cf. A008683, A008836 (Dirichlet inverse).
Cf. A179211, A179212, A179213, A179214, A179215. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 05 2010]
Cf. A020639.
Sequence in context: A157657 A008683 * A080323 A069158 A133639 A060038
Adjacent sequences: A008963 A008964 A008965 * A008967 A008968 A008969
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KEYWORD
| easy,nonn,mult
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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