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 A080999 Centrality of A080997(n) = a(n)/(A080997(n))^2. 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 23 11:05 EDT 2023. Contains 365544 sequences. (Running on oeis4.)