The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A050385 Reversion of Moebius function A008683. 8
 1, 1, 3, 10, 39, 160, 691, 3081, 14095, 65757, 311695, 1496833, 7266979, 35608419, 175875537, 874698246, 4376646808, 22016578909, 111282845162, 564886771380, 2878498888625, 14719219809915, 75505990358779, 388451973679785 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS From David W. Wilson, May 17 2017: (Start) Appears to equal the number of ways to partition Z into n residue classes. For example, a(4) = 10 since we can partition Z into 4 residue classes in 10 ways: Z = ∪ {0 (mod 2), 1 (mod 4), 3 (mod 8), 7 (mod 8)} Z = ∪ {0 (mod 2), 3 (mod 4), 1 (mod 8), 5 (mod 8)} Z = ∪ {0 (mod 2), 1 (mod 6), 3 (mod 6), 5 (mod 6)} Z = ∪ {1 (mod 2), 0 (mod 4), 2 (mod 8), 6 (mod 8)} Z = ∪ {1 (mod 2), 2 (mod 4), 0 (mod 8), 4 (mod 8)} Z = ∪ {1 (mod 2), 0 (mod 6), 2 (mod 6), 4 (mod 6)} Z = ∪ {0 (mod 3), 1 (mod 3), 2 (mod 6), 5 (mod 6)} Z = ∪ {0 (mod 3), 2 (mod 3), 1 (mod 6), 4 (mod 6)} Z = ∪ {1 (mod 3), 2 (mod 3), 0 (mod 6), 3 (mod 6)} Z = ∪ {0 (mod 4), 1 (mod 4), 2 (mod 4), 3 (mod 4)} (End) Unfortunately this conjecture is not correct; it fails at a(13). - Jeffrey Shallit, Nov 19 2017 The correct statement is that a(n) is the number of "natural exact covering systems" of cardinality n. These are covering systems (like the ones in David W. Wilson's comment) that are obtained by starting with the size-1 system x == 0 (mod 1) and successively choosing a congruence and "splitting" it into r >= 2 new congruences. - Jeffrey Shallit, Dec 07 2017 LINKS David W. Wilson, Table of n, a(n) for n = 1..1000 Yu Hin (Gary) Au, Decompositions of Unit Hypercubes and the Reversion of a Generalized Möbius Series, arXiv:2205.03680 [math.CO], 2022. I. P. Goulden, Andrew Granville, L. Bruce Richmond, and J. Shallit, Natural exact covering systems and the reversion of the Möbius series, Ramanujan J. (2019) Vol. 50, 211-235. I. P. Goulden, L. B. Richmond, and J. Shallit, Natural exact covering systems and the reversion of the Möbius series, arXiv:1711.04109 [math.NT], 2017-2018. N. J. A. Sloane, Transforms FORMULA G.f. A(x) satisfies: A(x) = x - Sum_{k>=2} mu(k) * A(x)^k. - Ilya Gutkovskiy, Apr 22 2020 MATHEMATICA InverseSeries[Sum[MoebiusMu[n] x^n, {n, 0, 25}] + O[x]^25] // CoefficientList[#, x]& // Rest (* Jean-François Alcover, Sep 29 2018 *) CROSSREFS Cf. A008683, A050386, A294672, A295162. Sequence in context: A151067 A007163 A219263 * A296195 A123768 A005750 Adjacent sequences: A050382 A050383 A050384 * A050386 A050387 A050388 KEYWORD nonn,nice AUTHOR Christian G. Bower, Nov 15 1999 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 7 01:51 EST 2022. Contains 358649 sequences. (Running on oeis4.)