A285057 a(n) = lcm(n, A001177(n)).

1, 6, 12, 12, 5, 12, 56, 24, 36, 30, 110, 12, 91, 168, 60, 48, 153, 36, 342, 60, 168, 330, 552, 24, 25, 546, 108, 168, 406, 60, 930, 96, 660, 306, 280, 36, 703, 342, 1092, 120, 820, 168, 1892, 660, 180, 552, 752, 48, 392, 150, 612, 1092, 1431, 108, 110, 168, 684, 1218, 3422, 60

Offset: 1

Author

Michel Marcus, Apr 09 2017

Keywords

• nonn

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..5000
• Paolo Leonetti, Carlo Sanna, On the greatest common divisor of n and the nth Fibonacci number, arXiv:1704.00151 [math.NT], 2017. See l(n) on page 2.

Crossrefs

Cf. A001177.

Programs

Mathematica

z[n_]:=Block[{k=1}, While[Mod[Fibonacci[k], n]!=0, k ++]; k]; a[n_]:=LCM[n, z[n]]; Table[a[n], {n, 100}] (* Indranil Ghosh, Apr 09 2017 *)

PARI

z(n) = {my(k = 1); while (fibonacci(k) % n, k++); k;}
a(n) = lcm(n, z(n));

Python

from sympy import fibonacci, lcm
def z(n):
    k=1
    while fibonacci(k)%n: k+=1
    return k
def a(n): return lcm(n, z(n))
print([a(n) for n in range(1,201)]) # Indranil Ghosh, Apr 09 2017

Formula

For p prime (except 5), a(p) = p*A001177(p). See Leonetti & Sanna link.