OFFSET
1,4
COMMENTS
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
LINKS
Wikipedia, Young tableau
EXAMPLE
The a(96) = 19 tableaux:
111112
.
111 1111 1112 11111 11112
112 12 11 2 1
.
11 111 111 112 1111 1112
11 11 12 11 1 1
12 2 1 1 2 1
.
11 11 111 112
11 12 1 1
1 1 1 1
2 1 2 1
.
11 12
1 1
1 1
1 1
2 1
.
1
1
1
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[primeMS, Join@@Permutations/@facs[n], {2}]];
Table[Length[Select[ptnplane[y], And[And@@LessEqual@@@#, And@@(LessEqual@@@Transpose[PadRight[#]/.(0->Infinity)])]&]], {y, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 16 2019
STATUS
approved