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

1,1

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

Formula

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A089497 A355937 A345950 * A333248 A114592 A344864

Adjacent sequences: A122892 A122893 A122894 * A122896 A122897 A122898

Keyword

easy,nonn

Author

Giovanni Teofilatto, Oct 24 2006

Extensions

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

Status

approved