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A323587 Number of strict (distinct parts) plane partitions of n with relatively prime parts.

%I A323587 #5 Jan 20 2019 23:19:44
%S A323587 1,1,0,2,2,4,6,10,12,18,30,40,48,74,92,142,172,242,294,412,490,722,
%T A323587 854,1164,1396,1880,2260,2976,3748,4764,5792,7472,9082,11488,14012,
%U A323587 17522,21830,26896,32820,40536,49488,60636,73626,89962,108854,134240,160952,195858
%N A323587 Number of strict (distinct parts) plane partitions of n with relatively prime parts.
%F A323587 Moebius transform of A117433.
%e A323587 The a(9) = 18 plane partitions:
%e A323587   81   72   621   54   531   432
%e A323587 .
%e A323587   8   7   61   62   5   51   53   42   43
%e A323587   1   2   2    1    4   3    1    3    2
%e A323587 .
%e A323587   6   5   4
%e A323587   2   3   3
%e A323587   1   1   2
%t A323587 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A323587 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A323587 ptnplane[n_]:=Union[Map[Reverse@*primeMS,Join@@Permutations/@facs[n],{2}]];
%t A323587 Table[Sum[Length[Select[ptnplane[Times@@Prime/@y],And[And@@GreaterEqual@@@#,And@@(GreaterEqual@@@Transpose[PadRight[#]])]&]],{y,Select[IntegerPartitions[n],UnsameQ@@#&&GCD@@#==1&]}],{n,30}]
%Y A323587 Cf. A000219, A000837, A003293, A006951, A026007, A100883, A117433 (strict plane partitions), A300275 (plane partitions with relatively prime parts), A303546, A320802, A323584, A323585.
%K A323587 nonn
%O A323587 0,4
%A A323587 _Gus Wiseman_, Jan 20 2019