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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.
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%I #10 Apr 26 2024 05:58:06

%S 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 85,89,93,102,103,107,111,117,121,123,132,139,167,171,177,179,181,187,

%U 201,205,207,213,219,221,233,241,246,247,253,257,262,267,269,273,279,281,282,293,295

%N 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 Numbers m such that A022307(m) = A086598(m).

%H Amiram Eldar, <a href="/A335002/b335002.txt">Table of n, a(n) for n = 1..134</a>

%H Prapanpong Pongsriiam, <a href="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 (PARI) lucas(n) = fibonacci(n+1)+fibonacci(n-1);

%o isok(m) = omega(fibonacci(m))==omega(lucas(m));

%Y Cf. A001221, A000032, A000045, A022307, A086598, A335001.

%K nonn

%O 1,2

%A _Michel Marcus_, May 19 2020