A007557 Shifts left when inverse Moebius transform applied twice. (Formerly M2458)

1, 1, 3, 5, 10, 12, 24, 26, 43, 52, 78, 80, 133, 135, 189, 219, 295, 297, 428, 430, 584, 642, 804, 806, 1100, 1123, 1395, 1494, 1856, 1858, 2428, 2430, 2977, 3143, 3739, 3811, 4790, 4792, 5654, 5930, 7072, 7074, 8656

Offset

1,3

Comments

Equals eigensequence of triangle A127170 (the square of the inverse Mobius transform). - Gary W. Adamson, Apr 27 2009

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, arXiv:math/0205301 [math.CO], 2002; Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]

M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]

N. J. A. Sloane, Transforms

Formula

a(n+1) = Sum_{d divides n} tau(n/d)*a(d). - Vladeta Jovovic, Jan 24 2003

From Ilya Gutkovskiy, Apr 30 2019: (Start)

G.f. A(x) satisfies: A(x) = x * (1 + Sum_{i>=1} Sum_{j>=1} A(x^(i*j))).

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)

Mathematica

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 *)

Crossrefs

Cf. A000005, A007554, A038045, A038046, A003238, A070965.

Cf. A127170. - Gary W. Adamson, Apr 27 2009

Sequence in context: A093661 A080561 A266663 * A034746 A345176 A275219

Adjacent sequences: A007554 A007555 A007556 * A007558 A007559 A007560

Keyword

nonn,nice,eigen

Author

N. J. A. Sloane

Extensions

More terms from Vladeta Jovovic, Jan 24 2003

Status

approved