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

1, 1, 0, 2, 2, 4, 6, 10, 12, 18, 30, 40, 48, 74, 92, 142, 172, 242, 294, 412, 490, 722, 854, 1164, 1396, 1880, 2260, 2976, 3748, 4764, 5792, 7472, 9082, 11488, 14012, 17522, 21830, 26896, 32820, 40536, 49488, 60636, 73626, 89962, 108854, 134240, 160952, 195858

Offset: 0

Author

Gus Wiseman, Jan 20 2019

Keywords

• nonn

Examples

			The a(9) = 18 plane partitions:
  81   72   621   54   531   432
.
  8   7   61   62   5   51   53   42   43
  1   2   2    1    4   3    1    3    2
.
  6   5   4
  2   3   3
  1   1   2
		

Crossrefs

Cf. A000219, A000837, A003293, A006951, A026007, A100883, A117433 (strict plane partitions), A300275 (plane partitions with relatively prime parts), A303546, A320802, A323584, A323585.

Programs

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[And@@GreaterEqual@@@#,And@@(GreaterEqual@@@Transpose[PadRight[#]])]&]],{y,Select[IntegerPartitions[n],UnsameQ@@#&&GCD@@#==1&]}],{n,30}]

Formula

Moebius transform of A117433.