A007554 Unique attractor for (RIGHT then MOBIUS) transform.

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

Author

N. J. A. Sloane

Keywords

• sign
• nice
• eigen
• look

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

Crossrefs

Cf. A003238.

Cf. A054525.

Cf. A027750, A008683.

Programs

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

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 *)

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