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A295391 a(1) = 2; a(n+1) = 1 + (a(n)^2 - a(n))*(1+1/n) for n >= 1. 1

%I

%S 2,5,31,1241,1923551,4440055831261,22999778415495431257188671,

%T 604559779613588034852176053517136070371409409780081,

%U 411179093017233901729922229390651516928263091167446329166300037456998815010841080003014976133796409791

%N a(1) = 2; a(n+1) = 1 + (a(n)^2 - a(n))*(1+1/n) for n >= 1.

%C (a(1), ..., a(n-1), a(n)-1) is an integer solution to the equation Sum_{k=1}^n k/x(k) = 1.

%H Robert Israel, <a href="/A295391/b295391.txt">Table of n, a(n) for n = 1..12</a>

%H R. Israel, <a href="https://math.stackexchange.com/questions/2531306/set-of-solutions-to-a-sum/2531415#2531415">Set of solutions to a sum</a>, Mathematics StackExchange.

%e 1/1 = 1.

%e 1/2 + 2/4 = 1.

%e 1/2 + 2/5 + 3/30 = 1.

%e 1/2 + 2/5 + 3/31 + 4/1240 = 1.

%e 1/2 + 2/5 + 3/31 + 4/1241 + 5/1923550 = 1.

%p a[1]:= 2:

%p for n from 1 to 10 do a[n+1]:= 1 + (a[n]^2 - a[n])*(1+1/n) od:

%p seq(a[i],i=1..11);

%t Fold[Append[#1, 1 + (Last[#1]^2 - Last[#1]) (1 + 1/#2)] &, {2}, Range@ 8] (* _Michael De Vlieger_, Nov 21 2017 *)

%K nonn

%O 1,1

%A _Robert Israel_, Nov 21 2017

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Last modified August 9 04:39 EDT 2020. Contains 336319 sequences. (Running on oeis4.)