OFFSET
1,3
COMMENTS
The diagram of a connected skew partition is required to be connected as a polyomino but can have empty rows or columns. A generalized Young tableau of shape y is an array obtained by replacing the dots in the Ferrers diagram of y with positive integers. A tableau is normal if its entries span an initial interval of positive integers. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
EXAMPLE
The a(9) = 11 tableaux:
1 1
1 1
.
2 1 1 1 1 1 1 2
1 1 1 2 2 2 1 2
.
1 1 1 2 1 2 1 3
2 3 1 3 3 3 2 3
.
1 2 1 3
3 4 2 4
MATHEMATICA
undcon[y_]:=Select[Tuples[Range[0, #]&/@y], Function[v, GreaterEqual@@v&&With[{r=Select[Range[Length[y]], y[[#]]=!=v[[#]]&]}, Or[Length[r]<=1, And@@Table[v[[i]]<y[[i+1]], {i, Range[Min@@r, Max@@r-1]}]]]]];
cos[y_]:=cos[y]=With[{sam=Most[undcon[y]]}, If[Length[sam]===0, If[Total[y]===0, {{}}, {}], Join@@Table[Prepend[#, y]&/@cos[sam[[k]]], {k, 1, Length[sam]}]]];
primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[Length[cos[Reverse[primeMS[n]]]], {n, 50}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 25 2018
STATUS
approved