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 A020652 Numerators in canonical bijection from positive integers to positive rationals. 28
 1, 1, 2, 1, 3, 1, 2, 3, 4, 1, 5, 1, 2, 3, 4, 5, 6, 1, 3, 5, 7, 1, 2, 4, 5, 7, 8, 1, 3, 7, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 5, 7, 11, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 3, 5, 9, 11, 13, 1, 2, 4, 7, 8, 11, 13, 14, 1, 3, 5, 7, 9, 11, 13, 15, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 1, 5 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS a(A002088(n)) = 1 for n > 1. - Reinhard Zumkeller, Jul 29 2012 When read as an irregular table with each 1 entry starting a new row, then the n-th row consists of the set of multiplicative units of Z_{n+1}. These rows form a group under multiplication mod n. - Tom Edgar, Aug 20 2013 REFERENCES S. Cook, Problem 511: An Enumeration Problem, Journal of Recreational Mathematics, Vol. 9:2 (1976-77), 137. Solution by the Problem Editor, JRM, Vol. 10:2 (1977-78), 122-123. Richard Courant and Herbert Robbins. What Is Mathematics?, Oxford, 1941, pp. 79-80. H. Lauwerier, Fractals, Princeton Univ. Press, p. 23. LINKS David Wasserman, Table of n, a(n) for n = 1..100000 Paul Yiu, Recreational Mathematics, 24.3.1 Appendix: Two enumerations of the rational numbers in (0,1), page 633. EXAMPLE Arrange positive fractions < 1 by increasing denominator then by increasing numerator: 1/2, 1/3, 2/3, 1/4, 3/4, 1/5, 2/5, 3/5, 4/5, 1/6 ... (this is A020652/A038567). - William Rex Marshall, Dec 16 2010 MAPLE with (numtheory): A020652 := proc (n) local sum, j, k; sum := 0: k := 2: while (sum < n) do: sum := sum + phi(k): k := k + 1: od: sum := sum - phi(k-1): j := 1; while sum < n do: if gcd(j, k-1) = 1 then sum := sum + 1: fi: j := j+1: od: RETURN (j-1): end: # Ulrich Schimke (ulrschimke(AT)aol.com), Nov 06 2001 MATHEMATICA Reap[Do[If[GCD[num, den] == 1, Sow[num]], {den, 1, 20}, {num, 1, den-1}] ][[2, 1]] (* Jean-François Alcover, Oct 22 2012 *) PROG (Haskell) a020652 n = a020652_list !! (n-1) a020652_list = map fst [(u, v) | v <- [1..], u <- [1..v-1], gcd u v == 1] -- Reinhard Zumkeller, Jul 29 2012 (PARI) a(n)=my(s, j=1, k=1); while(s

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Last modified December 12 14:27 EST 2018. Contains 318075 sequences. (Running on oeis4.)