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%I #30 Jan 20 2020 01:31:01
%S 1,2,10,12,20,20,54,96,132,171,222,458,520,731,1083
%N Start of n consecutive indices k such that Fibonacci(k) contains distinct number of divisors.
%C a(16) > 1443, if it exists. - _Chai Wah Wu_, Jan 19 2020
%e The 4th number of this sequence, 12, means that:
%e Fibonacci(12) = 144 = 2 ^ 4 * 3 ^ 2,
%e Fibonacci(13) = 233 (prime number),
%e Fibonacci(14) = 377 = 13 * 29,
%e Fibonacci(15) = 610 = 2 * 5 * 61,
%e and these Fibonacci numbers have distinct number of divisors: 15, 2, 4 and 8, respectively.
%p with(combinat, fibonacci):with(numtheory): for n from 1 to 10 do: i:=0:for k from 1 to 1500 while(i=0) do: lst:={}:for p from 0 to n-1 do :x:= fibonacci(k+p):y:=divisors(x):n1:=nops(y):lst:= lst union {n1}:od:if nops(lst)=n then printf(`%d, `,k): i:=1:else fi:od:od:
%Y Cf. A000045, A063375.
%K nonn,hard,more
%O 1,2
%A _Michel Lagneau_, Aug 08 2011
%E a(12)-a(15) from _Amiram Eldar_, Oct 18 2019