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A335001 Integers m such that d(F(m)) = d(L(m)) where d is the number of divisors function, F(n) and L(n) are respectively the n-th Fibonacci and n-th Lucas numbers.

%I A335001 #15 Jan 05 2025 19:51:41
%S A335001 1,4,5,7,10,11,13,14,17,18,26,46,47,58,73,77,85,89,103,107,121,139,
%T A335001 167,179,181,187,205,221,233,241,247,253,257,262,269,273,281,293,295,
%U A335001 317,329,335,337,341,371,377,397,407,409,427,442,454,466,491,506,563,611
%N A335001 Integers m such that d(F(m)) = d(L(m)) where d is the number of divisors function, F(n) and L(n) are respectively the n-th Fibonacci and n-th Lucas numbers.
%C A335001 Numbers m such that A063375(m) = A272377(m).
%C A335001 It appears that this is a subsequence of A335002, so that terms also satisfy omega(F(m)) = omega(L(m))
%H A335001 Amiram Eldar, <a href="/A335001/b335001.txt">Table of n, a(n) for n = 1..87</a>
%H A335001 Prapanpong Pongsriiam, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/57-5/pongsriiam.pdf">Fibonacci and Lucas Numbers which have Exactly Three Prime Factors and Some Unique Properties of F18 and L18</a>, Fibonacci Quart. 57 (2019), no. 5, 130-144.
%o A335001 (PARI) lucas(n) = fibonacci(n+1)+fibonacci(n-1);
%o A335001 isok(m) = numdiv(fibonacci(m))==numdiv(lucas(m));
%Y A335001 Cf. A000005, A000032, A000045, A063375, A272377, A335002.
%K A335001 nonn
%O A335001 1,2
%A A335001 _Michel Marcus_, May 19 2020