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 A303551 Number of aperiodic multisets of compositions of total weight n. 6
 1, 2, 6, 15, 41, 95, 243, 567, 1366, 3189, 7532, 17428, 40590, 93465, 215331, 493150, 1127978, 2569049, 5841442, 13240351, 29953601, 67596500, 152258270, 342235866, 767895382, 1719813753, 3845442485, 8584197657, 19133459138, 42583565928, 94641591888 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A multiset is aperiodic if its multiplicities are relatively prime. LINKS Andrew Howroyd, Table of n, a(n) for n = 1..1000 FORMULA a(n) = Sum_{d|n} mu(d) * A034691(n/d). EXAMPLE The a(4) = 15 aperiodic multisets of compositions are: {4}, {31}, {22}, {211}, {13}, {121}, {112}, {1111}, {1,3}, {1,21}, {1,12}, {1,111}, {2,11}, {1,1,2}, {1,1,11}. Missing from this list are {1,1,1,1}, {2,2}, and {11,11}. MAPLE with(numtheory): b:= proc(n) option remember; `if`(n=0, 1, add(add(       d*2^(d-1), d=divisors(j))*b(n-j), j=1..n)/n)     end: a:= n-> add(mobius(d)*b(n/d), d=divisors(n)): seq(a(n), n=1..35);  # Alois P. Heinz, Apr 26 2018 MATHEMATICA nn=20; ser=Product[1/(1-x^n)^2^(n-1), {n, nn}] Table[Sum[MoebiusMu[d]*SeriesCoefficient[ser, {x, 0, n/d}], {d, Divisors[n]}], {n, 1, nn}] PROG (PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)} seq(n)={my(u=EulerT(vector(n, n, 2^(n-1)))); vector(n, n, sumdiv(n, d, moebius(d)*u[n/d]))} \\ Andrew Howroyd, Sep 15 2018 CROSSREFS Cf. A000740, A000837, A007716, A007916, A034691, A100953, A255906, A269134, A301700, A303386, A303431, A303546, A303552. Sequence in context: A061322 A004664 A074446 * A180666 A280788 A121328 Adjacent sequences:  A303548 A303549 A303550 * A303552 A303553 A303554 KEYWORD nonn AUTHOR Gus Wiseman, Apr 26 2018 STATUS approved

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Last modified September 28 08:36 EDT 2021. Contains 347713 sequences. (Running on oeis4.)