%N Numbers n such that n and Lucas(n) have the same number of divisors.
%C All prime terms of A001606 (i.e., terms in A001606 that are not nontrivial powers of 2) are terms of this sequence.
%C Conjecture: all terms are of the form 2^k*p for k >= 0 and p prime.
%C It is unknown whether 1816 is a term (the smallest number for which membership in the sequence is unknown); it depends on whether Lucas(1816)/47 is a semiprime or not. The following composite numbers are terms of the sequence: 3106, 3928, 4006, 5414, 5498, 14318, 20578. - _Chai Wah Wu_, Jan 03 2020
%H Blair Kelly, <a href="http://mersennus.net/fibonacci/">Fibonacci and Lucas Factorizations</a>.
%t Select[Range,DivisorSigma[0,#]==DivisorSigma[0,LucasL[#]]&] (* _Metin Sariyar_, Jan 03 2020 *)
%o (PARI) for(k=1,320,if(numdiv(k)==numdiv(fibonacci(k+1)+fibonacci(k-1)),print1(k,", "))) \\ _Hugo Pfoertner_, Jan 03 2020
%Y Cf. A000032, A001606, A080651.
%A _Chai Wah Wu_, Dec 31 2019