A330777 Numbers k such that k and Lucas(k) have the same number of divisors.

1, 2, 5, 7, 10, 11, 13, 14, 17, 19, 24, 26, 28, 31, 37, 38, 40, 41, 47, 53, 61, 62, 71, 79, 86, 88, 113, 152, 178, 202, 248, 313, 353, 458, 488, 503, 586, 613, 617, 856, 863, 914, 1082, 1097, 1306, 1318, 1361, 1784

Offset

1,2

Comments

All prime terms of A001606 (i.e., terms in A001606 that are not nontrivial powers of 2) are terms of this sequence.

Conjecture: all terms are of the form 2^k*p for k >= 0 and p prime.

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

Links

Table of n, a(n) for n=1..48.

Blair Kelly, Fibonacci and Lucas Factorizations.

Mathematica

Select[Range[100], DivisorSigma[0, #]==DivisorSigma[0, LucasL[#]]&] (* Metin Sariyar, Jan 03 2020 *)

Prog

(PARI) for(k=1, 320, if(numdiv(k)==numdiv(fibonacci(k+1)+fibonacci(k-1)), print1(k, ", "))) \\ Hugo Pfoertner, Jan 03 2020

Crossrefs

Cf. A000032, A001606, A080651.

Sequence in context: A108118 A099477 A261034 * A259749 A067934 A284470

Adjacent sequences: A330774 A330775 A330776 * A330778 A330779 A330780

Keyword

nonn,more

Author

Chai Wah Wu, Dec 31 2019

Status

approved