

A193181


a(n) = lcm(f(1),f(2),...,f(n)) with f(x) = x^2+1.


3



2, 10, 10, 170, 2210, 81770, 408850, 408850, 16762850, 1693047850, 103275918850, 2995001646650, 2995001646650, 590015324390050, 66671731656075650, 17134635035611442050, 17134635035611442050, 17134635035611442050, 3101368941445671011050
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OFFSET

1,1


COMMENTS

log(a(n)) = n*log(n)+B*n+o(n); B=0.066275634213060706383563177025.
All prime factors of a(n) are in A002313.  Robert Israel, Mar 13 2016


LINKS

Robert Israel, Table of n, a(n) for n = 1..388
J. Cilleruelo, The least common multiple of a quadratic sequence, arXiv:1001.3438 [math.NT], 2010.
J. Cilleruelo, The least common multiple of a quadratic sequence, Compos. Math. 147 (2011), no. 4, 11291150.
Bakir Farhi, Nontrivial lower bounds for the least common multiple of some finite sequences of integers, J. Number Theory, 125 (2007), p. 393411.
Steven Finch, Cilleruelo's LCM Constants, 2013. [Cached copy, with permission of the author]
Juanjo Rué, Paulius Šarka, and Ana Zumalacárregui, On the error term of the logarithm of the lcm of a quadratic sequence, arXiv:1110.0939 [math.NT], 2011.
Juanjo Rué, Paulius Šarka, and Ana Zumalacárregui, On the error term of the logarithm of the lcm of a quadratic sequence, Journal de théorie des nombres de Bordeaux, 25 no. 2 (2013), p. 457470.
Index entries for sequences related to lcm's


MAPLE

a[0]:= 1:
for n from 1 to 30 do a[n]:= ilcm(a[n1], n^2+1) od:
seq(a[i], i=1..30); # Robert Israel, Mar 13 2016


MATHEMATICA

f[x_] := x^2+1; a[1] = f[1]; a[n_] := a[n] = LCM[f[n], a[n1]]; Table[a[n], {n, 20}]


PROG

(PARI) a(n)=lcm(vector(n, k, k^2+1)) \\ Charles R Greathouse IV, Jul 26 2013


CROSSREFS

Cf. A002313, A002522, A003418.
Sequence in context: A232500 A351659 A033466 * A338401 A222638 A299982
Adjacent sequences: A193178 A193179 A193180 * A193182 A193183 A193184


KEYWORD

nonn


AUTHOR

José María Grau Ribas, Jul 17 2011


STATUS

approved



