cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A075742 Fibonacci numbers for which both the value and index are the product of an odd number of distinct primes; that is, numbers Fibonacci(k) for which mu(k) = mu(Fibonacci(k)) = -1.

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%I A075742 #13 Mar 05 2025 22:05:15
%S A075742 2,5,13,89,233,1597,28657,514229,24157817,433494437,2971215073,
%T A075742 44945570212853,190392490709135,99194853094755497,
%U A075742 1500520536206896083277,3928413764606871165730,1066340417491710595814572169,19134702400093278081449423917
%N A075742 Fibonacci numbers for which both the value and index are the product of an odd number of distinct primes; that is, numbers Fibonacci(k) for which mu(k) = mu(Fibonacci(k)) = -1.
%e A075742 11 is a prime and Fibonacci(11) = 89 is a prime, 13 is a prime and Fibonacci(13) = 233 is a prime, but Fibonacci(16) = 987 = 3*7*47 and 16 is not squarefree and 30 = 2*3*5 is the product of an odd number of distinct primes but Fibonacci(30) = 832040 = 2^3*5*11*31*61 is not squarefree, ...
%p A075742 with(combinat, fibonacci): m2_supM_fib := proc(n); if (numtheory[mobius](n)=-1) then if (numtheory[mobius](fibonacci(n))=-1) then RETURN(fibonacci(n)); fi; fi; end:
%Y A075742 Cf. A000045, A008683, A030059, A074691.
%K A075742 easy,nonn
%O A075742 1,1
%A A075742 _Jani Melik_, Oct 07 2002
%E A075742 Incorrect 83621143489848422977 removed and more terms from _Sean A. Irvine_, Mar 05 2025