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%I #39 Oct 19 2018 03:28:54
%S 2,10,10,170,2210,81770,408850,408850,16762850,1693047850,
%T 103275918850,2995001646650,2995001646650,590015324390050,
%U 66671731656075650,17134635035611442050,17134635035611442050,17134635035611442050,3101368941445671011050
%N a(n) = lcm(f(1),f(2),...,f(n)) with f(x) = x^2+1.
%C log(a(n)) = n*log(n)+B*n+o(n); B=-0.066275634213060706383563177025.
%C All prime factors of a(n) are in A002313. - _Robert Israel_, Mar 13 2016
%H Robert Israel, <a href="/A193181/b193181.txt">Table of n, a(n) for n = 1..388</a>
%H J. Cilleruelo, <a href="http://arxiv.org/abs/1001.3438">The least common multiple of a quadratic sequence</a>, arXiv:1001.3438 [math.NT], 2010.
%H J. Cilleruelo, <a href="http://dx.doi.org/10.1112/S0010437X10005191">The least common multiple of a quadratic sequence</a>, Compos. Math. 147 (2011), no. 4, 1129-1150.
%H Bakir Farhi, <a href="https://doi.org/10.1016/j.jnt.2006.10.017">Nontrivial lower bounds for the least common multiple of some finite sequences of integers</a>, J. Number Theory, 125 (2007), p. 393-411.
%H Steven Finch, <a href="/A003418/a003418.pdf">Cilleruelo's LCM Constants</a>, 2013. [Cached copy, with permission of the author]
%H Juanjo Rué, Paulius Šarka, and Ana Zumalacárregui, <a href="http://arxiv.org/abs/1110.0939">On the error term of the logarithm of the lcm of a quadratic sequence</a>, arXiv:1110.0939 [math.NT], 2011.
%H Juanjo Rué, Paulius Šarka, and Ana Zumalacárregui, <a href="http://dx.doi.org/10.5802/jtnb.843">On the error term of the logarithm of the lcm of a quadratic sequence</a>, Journal de théorie des nombres de Bordeaux, 25 no. 2 (2013), p. 457-470.
%H <a href="/index/Lc#lcm">Index entries for sequences related to lcm's</a>
%p a[0]:= 1:
%p for n from 1 to 30 do a[n]:= ilcm(a[n-1],n^2+1) od:
%p seq(a[i],i=1..30); # _Robert Israel_, Mar 13 2016
%t f[x_] := x^2+1; a[1] = f[1]; a[n_] := a[n] = LCM[f[n],a[n-1]]; Table[a[n], {n,20}]
%o (PARI) a(n)=lcm(vector(n,k,k^2+1)) \\ _Charles R Greathouse IV_, Jul 26 2013
%Y Cf. A002313, A002522, A003418.
%K nonn
%O 1,1
%A _José María Grau Ribas_, Jul 17 2011
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