This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A330777 #28 Jun 26 2021 01:52:54 %S A330777 1,2,5,7,10,11,13,14,17,19,24,26,28,31,37,38,40,41,47,53,61,62,71,79, %T A330777 86,88,113,152,178,202,248,313,353,458,488,503,586,613,617,856,863, %U A330777 914,1082,1097,1306,1318,1361,1784 %N A330777 Numbers k such that k and Lucas(k) have the same number of divisors. %C A330777 All prime terms of A001606 (i.e., terms in A001606 that are not nontrivial powers of 2) are terms of this sequence. %C A330777 Conjecture: all terms are of the form 2^k*p for k >= 0 and p prime. %C A330777 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 A330777 Blair Kelly, <a href="http://mersennus.net/fibonacci/">Fibonacci and Lucas Factorizations</a>. %t A330777 Select[Range[100],DivisorSigma[0,#]==DivisorSigma[0,LucasL[#]]&] (* _Metin Sariyar_, Jan 03 2020 *) %o A330777 (PARI) for(k=1,320,if(numdiv(k)==numdiv(fibonacci(k+1)+fibonacci(k-1)),print1(k,", "))) \\ _Hugo Pfoertner_, Jan 03 2020 %Y A330777 Cf. A000032, A001606, A080651. %K A330777 nonn,more %O A330777 1,2 %A A330777 _Chai Wah Wu_, Dec 31 2019