A122895 Characteristic function of natural numbers with number of divisors equal to a Fibonacci number.

1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1

Offset: 1

Author

Giovanni Teofilatto, Oct 24 2006

Keywords

• easy
• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for characteristic functions
• Index entries for sequences computed from exponents in factorization of n

Crossrefs

Cf. A000005, A010056, A115568, A123193, A123240.

Programs

Mathematica

fibQ[n_] := IntegerQ@ Sqrt[5*n^2+4] || IntegerQ@ Sqrt[5*n^2-4]; Boole[ fibQ /@ DivisorSigma[0, Range[103]]] (* Giovanni Resta, Mar 10 2017 *)

PARI

isfib(n) = my(k=n^2); k+=(k+1)<<2; issquare(k) || (n>0 && issquare(k-8));
a(n) = isfib(numdiv(n)); \\ Michel Marcus, Mar 10 2017

Python

from sympy import divisor_count
from sympy.ntheory.primetest import is_square
def A122895(n): return int(is_square(m:=5*int(divisor_count(n))**2-4) or is_square(m+8)) # Chai Wah Wu, Oct 10 2023

Formula

a(n) = A010056(A000005(n)). - Chayim Lowen, Aug 01 2015

Extensions

a(0)=0 removed from data by Michel Marcus, Mar 10 2017