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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
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
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, 1129-1150.
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. 457-470.
MAPLE
a[0]:= 1:
for n from 1 to 30 do a[n]:= ilcm(a[n-1], 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[n-1]]; Table[a[n], {n, 20}]
PROG
(PARI) a(n)=lcm(vector(n, k, k^2+1)) \\ Charles R Greathouse IV, Jul 26 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved