

A330777


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


0



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
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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(k1)), 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



