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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 20 2019
STATUS
approved