A035105 - OEIS

%I #41 Jul 18 2022 03:09:39

%S 1,1,2,6,30,120,1560,10920,185640,2042040,181741560,1090449360,

%T 254074700880,7368166325520,449458145856720,21124532855265840,

%U 33735878969859546480,640981700427331383120,2679944489486672512824720,109877724068953573025813520

%N a(n) = LCM of Fibonacci sequence {F_1,...,F_n}.

%H Alois P. Heinz, <a href="/A035105/b035105.txt">Table of n, a(n) for n = 1..124</a>

%H Yuri V. Matiyasevich and Richard K. Guy, <a href="https://doi.org/10.1080/00029890.1986.11971904">A new formula for Pi</a>, The American Mathematical Monthly, Vol 93, No. 8 (1986), pp. 631-635.

%H Carlo Sanna, <a href="https://arxiv.org/abs/2007.13330">On the l.c.m. of shifted Fibonacci numbers</a>, arXiv:2007.13330 [math.NT], 2020.

%H <a href="/index/Lc#lcm">Index entries for sequences related to LCM's</a>

%F log(a(n)) ~ 3*n^2*log(phi)/Pi^2, where phi is the golden ratio, or equivalently lim_{n->oo} sqrt(6*log(A003266(n))/log(a(n))) = Pi. - _Amiram Eldar_, Jan 30 2019

%p a:= proc(n) option remember; `if`(n=1, 1,

%p       ilcm(a(n-1), combinat[fibonacci](n)))

%p     end:

%p seq(a(n), n=1..25);  # _Alois P. Heinz_, Feb 12 2018

%t a[ n_ ] := LCM@@Table[ Fibonacci[ k ], {k, 1, n} ]

%t With[{fibs=Fibonacci[Range[20]]},Table[LCM@@Take[fibs,n],{n, Length[ fibs]}]] (* _Harvey P. Dale_, Apr 29 2019 *)

%o (PARI) a(n)=lcm(apply(fibonacci,[1..n])) \\ _Charles R Greathouse IV_, Oct 07 2016

%o (Python)

%o from math import lcm

%o from sympy import fibonacci

%o def A035105(n): return lcm(*(fibonacci(i) for i in range(1,n+1))) # _Chai Wah Wu_, Jul 17 2022

%Y Cf. A000045, A001622, A003266, A059248.

%K nonn,easy

%O 1,3

%A Fred Schwab (fschwab(AT)nrao.edu)