A395811 Number of Fibonacci divisors of n that are at most sqrt(n).

1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 2, 2, 2, 2, 1, 4, 1, 2, 2, 2, 2, 3, 1, 2, 2, 3, 1, 3, 1, 2, 3, 2, 1, 3, 1, 3, 2, 2, 1, 3, 2, 2, 2, 2, 1, 4, 1, 2, 2, 3, 2, 3, 1, 2, 2, 3, 1, 4, 1, 2, 3, 2, 1, 3, 1, 4, 2, 2, 1, 3, 2, 2, 2

Offset

1,4

Comments

Counts the inferior Fibonacci divisors of n. The complementary divisors do not need to be Fibonacci.

Starts to differ from A333749 at n=36.

Links

Table of n, a(n) for n=1..87.

Formula

a(n) <= A038548(n).

Example

a(36)=3 counts the factorizations 1*36, 2*18 and 3*12 where 1, 2 and 3 are Fibonacci numbers. Factorizations 4*9 and 6*6 are not counted because 4 and 6 are not Fibonacci numbers.

Maple

A395811 := proc(n)
    local a, d;
    a := 0 ;
    for d in numtheory[divisors](n) do
        if d^2 <= n and isFib(d) then # isFib coded in A000045
            a := a+1 ;
        end if;
    end do:
    a ;
end proc:
seq(A395811(n), n=1..120) ;

Prog

(Python)
from sympy import divisors
from sympy.ntheory.primetest import is_square
isFib = lambda n: (lambda t: is_square(t + 4) or is_square(t - 4))(5 * (n ** 2))
def A395811(n):
  a = 0
  for i in divisors(n):
    if i ** 2 <= n and isFib(i):
      a += 1
  return a
print([A395811(x) for x in range(1, 88)]) # Aitzaz Imtiaz, May 13 2026, following the Maple program.

Crossrefs

Cf. A005086, A010056, A038548, A333749.

Sequence in context: A056171 A357328 A381401 * A333749 A238949 A383959

Adjacent sequences: A395806 A395807 A395810 * A395817 A395818 A395819

Keyword

nonn,less

Author

R. J. Mathar, May 07 2026

Status

approved