This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A323585 Third Moebius transform of A000219. Number of plane partitions of n whose multiset of rows is aperiodic and whose multiset of columns is also aperiodic and whose parts are relatively prime. 4
 1, 1, 0, 3, 7, 21, 30, 83, 129, 267, 428, 856, 1332, 2482, 3909, 6798, 10853, 18331, 28665, 47327, 73829, 118527, 183898, 290780, 446508, 695964, 1061290, 1631829, 2470970, 3759609, 5646952, 8512306, 12700005, 18972387, 28120953, 41690725, 61392966, 90379781 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS A multiset is aperiodic if its multiplicities are relatively prime. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..10000 FORMULA The Moebius transform T of a sequence q is T(q)(n) = Sum_{d|n} mu(n/d) * q(d) where mu = A008683. The first Moebius transform of A000219 is A300275 and the second is A323584. EXAMPLE The a(4) = 7 plane partitions with aperiodic multisets of rows and columns and relatively prime parts:   31   211 .   3   21   111   1   1    1 .   2   11   1   1   1   1 The same for a(5) = 21:   41   32   311   221   2111 .   4   3   31   21   22   21   211   111   1111   1   2   1    2    1    11   1     11    1 .   3   2   21   11   111   1   2   1    11   1   1   1   1    1    1 .   2   11   1   1   1   1   1   1 MATHEMATICA primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]; facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]]; ptnplane[n_]:=Union[Map[Reverse@*primeMS, Join@@Permutations/@facs[n], {2}]]; Table[Sum[Length[Select[ptnplane[Times@@Prime/@y], And[GCD@@Length/@Split[#]==1, GCD@@Length/@Split[Transpose[PadRight[#]]]==1, And@@GreaterEqual@@@#, And@@(GreaterEqual@@@Transpose[PadRight[#]])]&]], {y, Select[IntegerPartitions[n], GCD@@#==1&]}], {n, 10}] CROSSREFS Cf. A000219, A000837, A003293, A100953, A300275, A303546, A320802, A321390, A323584, A323587. Sequence in context: A018479 A090504 A018548 * A003585 A108102 A065523 Adjacent sequences:  A323582 A323583 A323584 * A323586 A323587 A323588 KEYWORD nonn AUTHOR Gus Wiseman, Jan 19 2019 STATUS approved

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

Last modified December 9 09:20 EST 2019. Contains 329877 sequences. (Running on oeis4.)