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A007436
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Moebius transform of Fibonacci numbers.
(Formerly M1023)
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6
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1, 0, 1, 2, 4, 6, 12, 18, 32, 50, 88, 134, 232, 364, 604, 966, 1596, 2544, 4180, 6708, 10932, 17622, 28656, 46206, 75020, 121160, 196384, 317432, 514228, 831374, 1346268, 2177322, 3524488, 5701290, 9227448, 14927632, 24157816, 39083988
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OFFSET
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1,4
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COMMENTS
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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
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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G.f.: Sum_{n>=1} a(n)*x^n/(1 - x^n) = x/(1 - x - x^2). - Ilya Gutkovskiy, Apr 25 2017
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MATHEMATICA
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mt[n_] := Block[{d = Divisors[n]}, Plus @@ (MoebiusMu /@ (n/d)*Fibonacci /@ d)]; Table[ mt[n], {n, 38}] (* Robert G. Wilson v Dec 10 2004 *)
a[n_] := DivisorSum[n, Fibonacci[#] MoebiusMu[n/#]&]; Array[a, 40] (* Jean-François Alcover, Dec 01 2015 *)
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PROG
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(PARI) a(n)=sumdiv(n, d, fibonacci(d)*moebius(n/d))
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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