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A323587 Number of strict (distinct parts) plane partitions of n with relatively prime parts. 4

%I #5 Jan 20 2019 23:19:44

%S 1,1,0,2,2,4,6,10,12,18,30,40,48,74,92,142,172,242,294,412,490,722,

%T 854,1164,1396,1880,2260,2976,3748,4764,5792,7472,9082,11488,14012,

%U 17522,21830,26896,32820,40536,49488,60636,73626,89962,108854,134240,160952,195858

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

%F Moebius transform of A117433.

%e The a(9) = 18 plane partitions:

%e 81 72 621 54 531 432

%e .

%e 8 7 61 62 5 51 53 42 43

%e 1 2 2 1 4 3 1 3 2

%e .

%e 6 5 4

%e 2 3 3

%e 1 1 2

%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];

%t facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];

%t ptnplane[n_]:=Union[Map[Reverse@*primeMS,Join@@Permutations/@facs[n],{2}]];

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

%K nonn

%O 0,4

%A _Gus Wiseman_, Jan 20 2019

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Last modified March 29 08:47 EDT 2024. Contains 371267 sequences. (Running on oeis4.)