144 is in the sequence because it is a Fibonacci number with 15 divisors and all smaller Fibonacci numbers have fewer divisors. - Emeric Deutsch, Jan 20 2009
MAPLE
with(numtheory): with(combinat): a := proc (n) if n = 1 then 1 else if max(seq(tau(fibonacci(j)), j = 1 .. n-1)) < tau(fibonacci(n)) then fibonacci(n) else end if end if end proc: seq(a(n), n = 1 .. 170); # Emeric Deutsch, Jan 20 2009
MATHEMATICA
DeleteDuplicates[{#, DivisorSigma[0, #]}&/@Fibonacci[Range[200]], GreaterEqual[#1[[2]], #2[[2]]]&][[;; , 1]] (* Harvey P. Dale, Aug 10 2025 *)
