A222463 - OEIS

%I #21 Oct 09 2023 02:21:39

%S 5,30,35,40,45,10,55,60,65,70,15,80,85,90,95,4,105,110,115,120,25,130,

%T 135,140,145,30,155,160,165,170,35,180,185,190,195,40,205,210,215,220,

%U 9,230,235,240,245,50,255,260,265,270,55,280,285,290,295,60

%N a(n) = n*5/gcd(n*5,n+5), n >= 5.

%C This is the fifth column (m=5) of the triangle A221918.

%H <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1).

%F a(n) = A221918(n,5) = numerator(n*5/(n+5)) = n*5/gcd(n*5,n+5) = n*5/gcd(25,n+5), n >= 5.

%F a(n) = 2*a(n-25)-a(n-50). - _Colin Barker_, Feb 25 2013

%F Sum_{k=5..n} a(k) ~ (521/250) * n^2. - _Amiram Eldar_, Oct 09 2023

%e a(10) = numerator(50/15) = numerator(10/3) = 10 = 50/gcd(50,15)= 50/5 = 50/gcd(25,15).

%t Table[(5n)/GCD[5n,n +5],{n,5,60}] (* _Harvey P. Dale_, Nov 06 2020 *)

%Y Cf. A221918, A000027 (m=1), A145979(m=2), A221920 (m=3), A221921 (m=4).

%K nonn,easy

%O 5,1

%A _Wolfdieter Lang_, Feb 21 2013