%I M2458 #38 May 11 2019 18:32:08
%S 1,1,3,5,10,12,24,26,43,52,78,80,133,135,189,219,295,297,428,430,584,
%T 642,804,806,1100,1123,1395,1494,1856,1858,2428,2430,2977,3143,3739,
%U 3811,4790,4792,5654,5930,7072,7074,8656
%N Shifts left when inverse Moebius transform applied twice.
%C Equals eigensequence of triangle A127170 (the square of the inverse Mobius transform). - _Gary W. Adamson_, Apr 27 2009
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Vincenzo Librandi, <a href="/A007557/b007557.txt">Table of n, a(n) for n = 1..1000</a>
%H M. Bernstein and N. J. A. Sloane, <a href="https://arxiv.org/abs/math/0205301">Some canonical sequences of integers</a>, arXiv:math/0205301 [math.CO], 2002; 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 divides n} tau(n/d)*a(d). - _Vladeta Jovovic_, Jan 24 2003
%F From _Ilya Gutkovskiy_, Apr 30 2019: (Start)
%F G.f. A(x) satisfies: A(x) = x * (1 + Sum_{i>=1} Sum_{j>=1} A(x^(i*j))).
%F G.f.: A(x) = Sum_{n>=1} a(n)*x^n = x * (1 + Sum_{i>=1} Sum_{j>=1} a(i)*x^(i*j)/(1 - x^(i*j))). (End)
%t a[n_] := a[n] = Sum[ DivisorSigma[0, (n - 1)/d]*a[d], {d, Divisors[n - 1]}]; a[1] = 1; Table[a[n], {n, 1, 43}] (* _Jean-François Alcover_, Dec 12 2011, after _Vladeta Jovovic_ *)
%Y Cf. A000005, A007554, A038045, A038046, A003238, A070965.
%Y Cf. A127170. - _Gary W. Adamson_, Apr 27 2009
%K nonn,nice,eigen
%O 1,3
%A _N. J. A. Sloane_
%E More terms from _Vladeta Jovovic_, Jan 24 2003