A080999 Centrality of A080997(n) = a(n)/(A080997(n))^2.

1, 3, 5, 8, 15, 9, 20, 40, 27, 13, 21, 45, 39, 63, 48, 72, 100, 21, 135, 25, 65, 104, 63, 168, 33, 180, 81, 75, 195, 112, 240, 65, 37, 360, 105, 117, 189, 168, 99, 45, 243, 260, 125, 420, 195, 111, 200, 520, 315, 351, 567, 273, 57, 432, 135, 61, 165, 256, 900, 189, 375

Offset: 1

Author

Matthew Vandermast, Mar 02 2003

Keywords

• nonn

Comments

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

Crossrefs

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

Formula

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.