A035105 a(n) = LCM of Fibonacci sequence {F_1,...,F_n}.

1, 1, 2, 6, 30, 120, 1560, 10920, 185640, 2042040, 181741560, 1090449360, 254074700880, 7368166325520, 449458145856720, 21124532855265840, 33735878969859546480, 640981700427331383120, 2679944489486672512824720, 109877724068953573025813520

Offset: 1

Author

Fred Schwab (fschwab(AT)nrao.edu)

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..124
• Yuri V. Matiyasevich and Richard K. Guy, A new formula for Pi, The American Mathematical Monthly, Vol 93, No. 8 (1986), pp. 631-635.
• Carlo Sanna, On the l.c.m. of shifted Fibonacci numbers, arXiv:2007.13330 [math.NT], 2020.
• Index entries for sequences related to LCM's

Crossrefs

Cf. A000045, A001622, A003266, A059248.

Programs

Maple

a:= proc(n) option remember; `if`(n=1, 1,
      ilcm(a(n-1), combinat[fibonacci](n)))
    end:
seq(a(n), n=1..25);  # Alois P. Heinz, Feb 12 2018

Mathematica

a[ n_ ] := LCM@@Table[ Fibonacci[ k ], {k, 1, n} ]
With[{fibs=Fibonacci[Range[20]]},Table[LCM@@Take[fibs,n],{n, Length[ fibs]}]] (* Harvey P. Dale, Apr 29 2019 *)

PARI

a(n)=lcm(apply(fibonacci,[1..n])) \\ Charles R Greathouse IV, Oct 07 2016

Python

from math import lcm
from sympy import fibonacci
def A035105(n): return lcm(*(fibonacci(i) for i in range(1,n+1))) # Chai Wah Wu, Jul 17 2022

Formula

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