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

1,2

Comments

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

Links

Table of n, a(n) for n=1..61.

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.

Crossrefs

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

Sequence in context: A108301 A282390 A095290 * A077579 A076797 A290630

Adjacent sequences: A080996 A080997 A080998 * A081000 A081001 A081002

Keyword

nonn

Author

Matthew Vandermast, Mar 02 2003

Status

approved