OFFSET
1,2
COMMENTS
The diagram of a connected skew partition is required to be connected as a polyomino but can have empty rows or columns.
EXAMPLE
The a(15) = 7 denominators are (), (1), (11), (22), (3), (31), (32) with diagrams:
o o o . o o . o o . . o . . . . . . o o o
o o o o . o . . o o . o o o
Missing are the two disconnected skew partitions:
. . o . . o
o o . o
MATHEMATICA
primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
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]}]]]]];
Table[Length[undcon[Reverse[primeMS[n]]]], {n, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 25 2018
STATUS
approved