OFFSET
0,4
COMMENTS
A multiset is aperiodic if its multiplicities are relatively prime.
Also the number of plane partitions of n whose multiset of rows is aperiodic and whose parts are relatively prime.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..10000
FORMULA
EXAMPLE
The a(4) = 8 plane partitions with aperiodic multisets of rows and columns:
4 31 211
.
3 21 111
1 1 1
.
2 11
1 1
1 1
The a(4) = 8 plane partitions with aperiodic multiset of rows and relatively prime parts:
31 211 1111
.
3 21 111
1 1 1
.
2 11
1 1
1 1
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[GCD@@Length/@Split[#]==1, And@@GreaterEqual@@@#, And@@(GreaterEqual@@@Transpose[PadRight[#]])]&]], {y, Select[IntegerPartitions[n], GCD@@#==1&]}], {n, 10}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 19 2019
STATUS
approved