%I A018804
%S A018804 1,3,5,8,9,15,13,20,21,27,21,40,25,39,45,48,33,63,37,72,65,63,45,100,
%T A018804 65,75,81,104,57,135,61,112,105,99,117,168,73,111,125,180,81,195,85,
%U A018804 168,189,135,93,240,133,195,165,200,105,243,189,260,185,171,117,360
%N A018804 Sum of gcd(k,n) for 1 <= k <= n.
%C A018804 a(n) is the number of times the number 1 appears in the character table 
               of the cyclic group C_n. - Ahmed Fares (ahmedfares(AT)my-deja.com), 
               Jun 02 2001
%C A018804 a(n) is the number of ways to express all fractions f/g whereby each 
               product (f/g)*n is a natural number between 1 and n (using fractions 
               of the form f/g with 1 <= f,g <= n). For example, for n=4 there are 
               8 such fractions: 1/1, 1/2, 2/2, 3/3, 1/4, 2/4, 3/4 and 4/4. - Ron 
               Lalonde (ronronronlalonde(AT)hotmail.com), Oct 03 2002
%C A018804 a(n) is the number of non-congruent solutions to xy = 0 mod n. - Yuval 
               Dekel (dekelyuval(AT)hotmail.com), Oct 06 2003
%C A018804 Equals row sums of triangle A127375 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Aug 27 2008]
%D A018804 J. O. Shallit, Problem E 2821, American Mathematical Monthly 87 (1980), 
               220. Solution in American Mathematical Monthly, 88 (1981), 444-445.
%H A018804 T. D. Noe, <a href="b018804.txt">Table of n, a(n) for n=1..2000</a>
%F A018804 a(n)=Sum_{d|n} d*phi(n/d), where phi(n) is Euler totient function (cf. 
               A000010) - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 04 2001
%F A018804 Multiplicative; for prime p, a(p^e) = p^(e-1)*((p-1)e+p).
%F A018804 Dirichlet g.f.: zeta(s-1)^2/zeta(s).
%F A018804 a(n)=Sum_{d|n} d*tau(d)*mu(n/d) - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Oct 23 2003
%F A018804 Equals A054523 * [1,2,3,...]. Equals row sums of triangle A010766. - 
               Gary W. Adamson (qntmpkt(AT)yahoo.com), May 20 2007
%F A018804 Equals Mobius transform of A029935 = A054525 * (1, 2, 4, 5, 8, 8, 12, 
               12,...). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 02 2008]
%F A018804 Equals row sums of triangle A127478 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Aug 03 2008]
%p A018804 a:=n->sum(igcd(n,j),j=1..n): seq(a(n), n=1..60); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Nov 05 2006
%o A018804 (PARI) a(n)=direuler(p=2,n,(1-X)/(1-p*X)^2)[n]
%Y A018804 Cf. A080997, A080998 for rankings of the positive integers in terms of 
               centrality, defined to be the average fraction of an integer that 
               it shares with the other integers as a gcd, or A018804(n)/n^2, also 
               A080999, a permutation of this sequence (A080999(n) = A018804(A080997(n))).
%Y A018804 Cf. A010766, A054523.
%Y A018804 A127468 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 03 2008]
%Y A018804 A127375 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 27 2008]
%Y A018804 Sequence in context: A050094 A137319 A138808 this_sequence A032682 A022769 
               A067241
%Y A018804 Adjacent sequences: A018801 A018802 A018803 this_sequence A018805 A018806 
               A018807
%K A018804 nonn,mult
%O A018804 1,2
%A A018804 David W. Wilson (davidwwilson(AT)comcast.net)