Search: id:A018805
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%I A018805
%S A018805 1,3,7,11,19,23,35,43,55,63,83,91,115,127,143,159,191,203,239,255,279,
%T A018805 299,343,359,399,423,459,483,539,555,615,647,687,719,767,791,863,899,947,
%U A018805 979,1059,1083,1167,1207,1255,1299,1391,1423,1507,1547,1611,1659,1763
%N A018805 Number of elements in the set {(x,y): 1<=x,y<=n, 1=gcd(x,y)}.
%C A018805 Equals partial sums of A140434 (1, 2, 4, 4, 8, 4, 12, 8,...) and row 
               sums of triangle A143469. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Aug 17 2008]
%D A018805 Cai, Jin-Yi and Bach, Eric. On testing for zero polynomials by a set 
               of points with bounded precision, Theoret. Comput. Sci. 296 (2003), 
               no. 1, 15-25. MR1965515 (2004m:68279).
%D A018805 S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 110-112.
%D A018805 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 
               3rd ed., Oxford Univ. Press, 1954.
%H A018805 Pieter Moree, <a href="http://arxiv.org/abs/math/0510003">Counting carefree 
               couples</a>
%H A018805 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               CarefreeCouple.html">Carefree Couple</a>
%F A018805 a(n) = 2*A015614(n) + 1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Apr 08 2006
%F A018805 a(n) = 2*A002088(n) - 1. - Hugo van der Sanden (hv(AT)crypt.org), Nov 
               22 2008
%F A018805 a(n) = 2 ( Sum phi(j), j=1..n ) - 1; a(n) = n^2 - Sum a([ n/j ]), j=2..n.
%F A018805 a(n) ~ (1/Zeta(2)) * n^2 = (6/pi^2) * n^2 as n goes to infinity (zeta 
               is the Riemann zeta function and the constant 6/pi^2 is 0.607927...). 
               - Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 18 2001
%F A018805 a(n)=sum(k=1, n, mu(k)*floor(n/k)^2) - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               May 11 2003
%t A018805 FoldList[ Plus, 1, 2 Array[ EulerPhi, 60, 2 ] ]
%Y A018805 Cf. A100613 (gcd > 1), A071778 (triples).
%Y A018805 A143469, A140434 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 17 
               2008]
%Y A018805 Sequence in context: A092109 A117991 A118260 this_sequence A135932 A105876 
               A141101
%Y A018805 Adjacent sequences: A018802 A018803 A018804 this_sequence A018806 A018807 
               A018808
%K A018805 nonn
%O A018805 1,2
%A A018805 David W. Wilson (davidwwilson(AT)comcast.net)
%E A018805 Mathematica program Aug 15 1997 (Olivier Gerard).
%E A018805 More terms from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Apr 08 2006
%E A018805 Link to Moree's paper corrected Peter Luschny (peter(AT)luschny.de), 
               Aug 08 2009

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