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A063659
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Numbers 1<=m<=n for which GCD(m,n) is not divisible by a square greater than 1.
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7
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1, 2, 3, 3, 5, 6, 7, 6, 8, 10, 11, 9, 13, 14, 15, 12, 17, 16, 19, 15, 21, 22, 23, 18, 24, 26, 24, 21, 29, 30, 31, 24, 33, 34, 35, 24, 37, 38, 39, 30, 41, 42, 43, 33, 40, 46, 47, 36, 48, 48, 51, 39, 53, 48, 55, 42, 57, 58, 59, 45, 61, 62, 56, 48, 65, 66, 67, 51, 69, 70, 71, 48
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Equals Mobius transform of A001615 - Gary W. Adamson (qntmpkt(AT)yahoo.com), May 23 2008
Apparently also the absolute values of the Dirichlet inverse of A007913. - R. J. Mathar, Dec 22 2010
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,2000
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FORMULA
| a(n)=n-A063658(n).
Multiplicative with a(p) = p and a(p^e) = p^e-p^(e-2), e>1. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 26 2001
a(n) = sum(d|n, phi(d)*moebius(n/d)^2 ), Dirichlet convolution of A000010 and A008966. - Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 08 2002
a(n)=sum(k=1,n,mu(gcd(n,k))^2) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 14 2007
Dirichlet g.f. zeta(s-1)/zeta(2s). - R. J. Mathar, Feb 27 2011
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EXAMPLE
| For n=12 we find only GCD(4,12), GCD(8,12) and GCD(12,12) divisible by 4, so a(12)=9.
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PROG
| (PARI) a(n)=sum(k=1, n, moebius(gcd(n, k))^2) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 14 2007
(PARI) { for (n=1, 2000, a=1; for (m=2, n, if (issquarefree(gcd(m, n)), a++)); write("b063659.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 27 2009]
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CROSSREFS
| Cf. A001615.
Sequence in context: A097248 A097247 A097246 * A115350 A187043 A081211
Adjacent sequences: A063656 A063657 A063658 * A063660 A063661 A063662
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KEYWORD
| mult,nonn
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AUTHOR
| Floor van Lamoen (fvlamoen(AT)hotmail.com), Jul 24 2001
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs) and Dean Hickerson, Jul 26, 2001
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