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A335002 Integers m such that omega(F(m)) = omega(L(m)) where omega is the number of distinct prime divisors function, F(n) and L(n) are the n-th Fibonacci and n-th Lucas numbers.

%I A335002 #11 Jan 05 2025 19:51:41
%S A335002 1,3,4,5,7,9,10,11,13,14,15,17,18,21,26,33,42,46,47,55,58,66,69,73,77,
%T A335002 85,89,93,102,103,107,111,117,121,123,132,139,167,171,177,179,181,187,
%U A335002 201,205,207,213,219,221,233,241,246,247,253,257,262,267,269,273,279,281,282,293,295
%N A335002 Integers m such that omega(F(m)) = omega(L(m)) where omega is the number of distinct prime divisors function, F(n) and L(n) are the n-th Fibonacci and n-th Lucas numbers.
%C A335002 Numbers m such that A022307(m) = A086598(m).
%H A335002 Amiram Eldar, <a href="/A335002/b335002.txt">Table of n, a(n) for n = 1..134</a>
%H A335002 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 A335002 (PARI) lucas(n) = fibonacci(n+1)+fibonacci(n-1);
%o A335002 isok(m) = omega(fibonacci(m))==omega(lucas(m));
%Y A335002 Cf. A001221, A000032, A000045, A022307, A086598, A335001.
%K A335002 nonn
%O A335002 1,2
%A A335002 _Michel Marcus_, May 19 2020