A123927 Characteristic function of natural numbers with number of divisors equal to a Lucas number.

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

Offset: 1

Author

Giovanni Teofilatto, Nov 22 2006

Keywords

• easy
• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for characteristic functions
• Index entries for sequences computed from exponents in factorization of n

Crossrefs

Cf. A000005, A102460, A119885, A119911, A122895.

Programs

Mathematica

With[{nn = 103}, Table[Boole[MemberQ[#, DivisorSigma[0, n]]], {n, nn}] &@ TakeWhile[Union@ Array[LucasL, 40, 0], # <= nn &]] (* Michael De Vlieger, Nov 22 2017 *)

PARI

A102460(n) = { my(u1=1,u2=3,old_u1); if(n<=2,sign(n),while(n>u2,old_u1=u1;u1=u2;u2=old_u1+u2);(u2==n)); };
A123927(n) = A102460(numdiv(n)); \\ Antti Karttunen, Nov 22 2017

Formula

a(n) = A102460(A000005(n)). - Antti Karttunen, Nov 22 2017

Extensions

Superfluous 0 at the beginning of data removed by Antti Karttunen, Nov 22 2017