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Numerators of harmonic mean H(n, 5), n >= 0.
1

%I #14 Sep 08 2022 08:46:05

%S 0,5,20,15,40,5,60,35,80,45,20,55,120,65,140,15,160,85,180,95,8,105,

%T 220,115,240,25,260,135,280,145,60,155,320,165,340,35,360,185,380,195,

%U 80,205,420,215,440,9,460,235,480,245,100,255,520,265,540,55,560

%N Numerators of harmonic mean H(n, 5), n >= 0.

%C a(n) = numerator(H(n, 5)) = numerator(10*n/(n+5)), n>=0, with H(n, 5) the harmonic mean of n and 5.

%C The corresponding denominator is given in A227108(n), n>= 0.

%C a(n+5), n>=0, is the fifth column (m=5) of the triangle A227041.

%F a(n) = numerator(10*n/(n+5)), n >= 0.

%F a(n) = 10*n/gcd(n+5,10*n) = 10*n/gcd(n+5,50), n >= 0.

%e The rationals H(n,5) begin: 0, 5/3, 20/7, 15/4, 40/9, 5, 60/11, 35/6, 80/13, 45/7, 20/3, 55/8, 120/17, 65/9, ...

%t Table[Numerator[(10 n / (n + 5))], {n, 0, 60}] (* _Vincenzo Librandi_, Nov 06 2016 *)

%o (PARI) a(n) = numerator(10*n/(n+5)); \\ _Michel Marcus_, Nov 06 2016

%o (Magma) [Numerator(10*n/(n+5)): n in [0..60]]; // _Vincenzo Librandi_, Nov 06 2016

%Y Cf. A227041(n+5,5), A227108 (denominator).

%K nonn,frac,easy

%O 0,2

%A _Wolfdieter Lang_, Jul 01 2013