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Centrality of A080997(n) = a(n)/(A080997(n))^2.
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%I #4 Mar 30 2012 17:27:18

%S 1,3,5,8,15,9,20,40,27,13,21,45,39,63,48,72,100,21,135,25,65,104,63,

%T 168,33,180,81,75,195,112,240,65,37,360,105,117,189,168,99,45,243,260,

%U 125,420,195,111,200,520,315,351,567,273,57,432,135,61,165,256,900,189,375

%N Centrality of A080997(n) = a(n)/(A080997(n))^2.

%C A permutation of sequence A018804, which gives the sum of gcd (k,n) for 1 <= k <= n.

%F The multiplicative formula for the numerator in a positive integer's centrality fraction is: for prime p, a(p^e)= p^(e-1)*((p-1)e+p) (cf. A018804). Dividing by the square of the integer gives the integer's centrality, which is defined to be the average fraction of the integer that it shares with the other integers as a gcd; see A080997 for other interpretations. This sequence gives the unreduced centrality numerators for A080997(n), where A080997 is the sequence of positive integers in nonincreasing order of their centrality.

%Y Cf. A080997, A080998 for centrality rankings of the positive integers.

%K nonn

%O 1,2

%A _Matthew Vandermast_, Mar 02 2003