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%I M1023 #30 Dec 26 2021 21:44:14
%S 1,0,1,2,4,6,12,18,32,50,88,134,232,364,604,966,1596,2544,4180,6708,
%T 10932,17622,28656,46206,75020,121160,196384,317432,514228,831374,
%U 1346268,2177322,3524488,5701290,9227448,14927632,24157816,39083988
%N Moebius transform of Fibonacci numbers.
%C After a(4) = 2, there are no primes in this sequence. Every element thereafter has at least two prime factors, the semiprimes (intersection of A007436 and A001358) starting 4, 6, 134, 831374, ... - _Jonathan Vos Post_, Dec 15 2004
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H T. D. Noe, <a href="/A007436/b007436.txt">Table of n, a(n) for n = 1..500</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F Row sums of the triangle generated by A054525 * A127647. - _Gary W. Adamson_, Jan 22 2007
%F G.f.: Sum_{n>=1} a(n)*x^n/(1 - x^n) = x/(1 - x - x^2). - _Ilya Gutkovskiy_, Apr 25 2017
%t mt[n_] := Block[{d = Divisors[n]}, Plus @@ (MoebiusMu /@ (n/d)*Fibonacci /@ d)]; Table[ mt[n], {n, 38}] (* _Robert G. Wilson v_ Dec 10 2004 *)
%t a[n_] := DivisorSum[n, Fibonacci[#] MoebiusMu[n/#]&]; Array[a, 40] (* _Jean-François Alcover_, Dec 01 2015 *)
%o (PARI) a(n)=sumdiv(n,d,fibonacci(d)*moebius(n/d))
%Y Cf. A001358.
%K nonn,easy
%O 1,4
%A _N. J. A. Sloane_
%E More terms from _Robert G. Wilson v_, Dec 10 2004
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