OFFSET
1,6
COMMENTS
LINKS
EXAMPLE
Triangle begins:
1
1
0 1
1 2
0 0 1
0 1 3
0 0 0 0 1
1 3 6
0 1 0 2 6
0 0 0 1 4
0 0 0 0 0 0 1
0 2 1 5 12
0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 1 5
0 0 0 1 0 3 10
1 6 4 12 24
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 1 5 2 12 30
For example, row 12 gives: e(211) = 2m(22) + m(31) + 5m(211) + 12m(1111).
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];
nrmptn[n_]:=Join@@MapIndexed[Table[#2[[1]], {#1}]&, If[n==1, {}, Flatten[Cases[FactorInteger[n]//Reverse, {p_, k_}:>Table[PrimePi[p], {k}]]]]];
Table[Table[Sum[Times@@Factorial/@Length/@Split[Sort[Length/@mtn, Greater]]/Times@@Factorial/@Length/@Split[mtn], {mtn, Select[mps[nrmptn[n]], And[And@@UnsameQ@@@#, Sort[Length/@#]==primeMS[k]]&]}], {k, Sort[Times@@Prime/@#&/@IntegerPartitions[Total[primeMS[n]]]]}], {n, 18}]
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, Nov 19 2018
STATUS
approved