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 A323584 Second Moebius transform of A000219. Number of plane partitions of n whose multiset of rows is aperiodic and whose multiset of columns is also aperiodic. 4
 1, 1, 1, 4, 8, 22, 34, 84, 137, 271, 450, 857, 1373, 2483, 3993, 6823, 10990, 18332, 28966, 47328, 74286, 118614, 184755, 290781, 448010, 695986, 1063773, 1632100, 2474970, 3759610, 5654233, 8512307, 12710995, 18973247, 28139285, 41690830, 61423271, 90379782 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS A multiset is aperiodic if its multiplicities are relatively prime. Also the number of plane partitions of n whose multiset of rows is aperiodic and whose parts 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 third is A323585. EXAMPLE The a(4) = 8 plane partitions with aperiodic multisets of rows and columns:   4   31   211 .   3   21   111   1   1    1 .   2   11   1   1   1   1 The a(4) = 8 plane partitions with aperiodic multiset of rows and relatively prime parts:   31   211   1111 .   3   21   111   1   1    1 .   2   11   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, And@@GreaterEqual@@@#, And@@(GreaterEqual@@@Transpose[PadRight[#]])]&]], {y, Select[IntegerPartitions[n], GCD@@#==1&]}], {n, 10}] CROSSREFS Cf. A000219, A000837, A003293, A100953, A300275, A303546, A320802, A321390, A323585, A323587. Sequence in context: A129794 A064503 A050482 * A200149 A153765 A003606 Adjacent sequences:  A323581 A323582 A323583 * A323585 A323586 A323587 KEYWORD nonn AUTHOR Gus Wiseman, Jan 19 2019 STATUS approved

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Last modified January 17 14:57 EST 2020. Contains 330958 sequences. (Running on oeis4.)