A193181 a(n) = lcm(f(1),f(2),...,f(n)) with f(x) = x^2+1.

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

Offset: 1

Author

José María Grau Ribas, Jul 17 2011

Keywords

• nonn

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, 1129-1150.
• Bakir Farhi, Nontrivial lower bounds for the least common multiple of some finite sequences of integers, J. Number Theory, 125 (2007), p. 393-411.
• 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.
• Index entries for sequences related to lcm's

Crossrefs

Cf. A002313, A002522, A003418.

Programs

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}]

PARI

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