A007554 Unique attractor for (RIGHT then MOBIUS) transform. (Formerly M0434)

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, 32, 29, 32, 32, 31, 30, 29, 21, 23, 11, 17, 5, 4, -13, -15, -28, -29, -52, -53, -76, -78, -104, -105, -142, -139, -168, -179, -209, -210, -253, -249, -278, -294

Offset

1,5

Comments

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]

References

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

Links

Franklin T. Adams-Watters, Table of n, a(n) for n = 1..5000

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 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|n} mu(n/d) * a(d).

G.f. A(x) satisfies: A(x) = x + x * Sum_{k>=1} mu(k) * A(x^k). - Ilya Gutkovskiy, Jul 01 2021

Mathematica

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 *)

Prog

(Haskell)
import Data.List (genericIndex)
a007554 n = genericIndex a007554_list (n-1)
a007554_list = 1 : f 1 where
   f x = (sum $ zipWith (*) (map a008683 divs)
                            (map a007554 $ reverse divs)) : f (x + 1)
          where divs = a027750_row x
-- Reinhard Zumkeller, Mar 16 2013

Crossrefs

Cf. A003238.

Cf. A054525, A143809. - Gary W. Adamson, Sep 01 2008

Cf. A027750, A008683.

Sequence in context: A278116 A352420 A215469 * A139069 A071866 A077603

Adjacent sequences: A007551 A007552 A007553 * A007555 A007556 A007557

Keyword

sign,nice,eigen,look

Author

N. J. A. Sloane

Status

approved