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%I M0434 #35 Jul 02 2021 16:43:36
%S 1,1,0,-1,-2,-3,-3,-4,-3,-3,-1,-2,3,2,5,8,12,11,17,16,21,25,26,25,30,
%T 32,29,32,32,31,30,29,21,23,11,17,5,4,-13,-15,-28,-29,-52,-53,-76,-78,
%U -104,-105,-142,-139,-168,-179,-209,-210,-253,-249,-278,-294
%N Unique attractor for (RIGHT then MOBIUS) transform.
%C Equals row sums of the eigentriangle A143809 of the Mobius transform;/Q and right border of A143809./Q A007554 = the eigensequence of the Mobius transform. [From _Gary W. Adamson_, Sep 01 2008]
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Franklin T. Adams-Watters, <a href="/A007554/b007554.txt">Table of n, a(n) for n = 1..5000</a>
%H M. Bernstein and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.CO/0205301">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
%H M. Bernstein and N. J. A. Sloane, <a href="/A003633/a003633_1.pdf">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F a(n+1) = Sum_{d|n} mu(n/d) * a(d).
%F G.f. A(x) satisfies: A(x) = x + x * Sum_{k>=1} mu(k) * A(x^k). - _Ilya Gutkovskiy_, Jul 01 2021
%t a[n_] := a[n] = Sum[ MoebiusMu[ (n - 1)/d]*a[d], {d, Divisors[n - 1]}]; a[1] = 1; Table[a[n], {n, 1, 58}] (* _Jean-François Alcover_, Jan 04 2012, from formula *)
%o (Haskell)
%o import Data.List (genericIndex)
%o a007554 n = genericIndex a007554_list (n-1)
%o a007554_list = 1 : f 1 where
%o f x = (sum $ zipWith (*) (map a008683 divs)
%o (map a007554 $ reverse divs)) : f (x + 1)
%o where divs = a027750_row x
%o -- _Reinhard Zumkeller_, Mar 16 2013
%Y Cf. A003238.
%Y Cf. A054525, A143809. - _Gary W. Adamson_, Sep 01 2008
%Y Cf. A027750, A008683.
%K sign,nice,eigen,look
%O 1,5
%A _N. J. A. Sloane_
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