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A323587
Number of strict (distinct parts) plane partitions of n with relatively prime parts.
4
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
0,4
FORMULA
Moebius transform of A117433.
EXAMPLE
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
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}]
CROSSREFS
Cf. A000219, A000837, A003293, A006951, A026007, A100883, A117433 (strict plane partitions), A300275 (plane partitions with relatively prime parts), A303546, A320802, A323584, A323585.
Sequence in context: A326448 A326528 A326633 * A236634 A034406 A098330
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 20 2019
STATUS
approved