OFFSET
1,3
COMMENTS
This multiset (row n of A305936) is generally not the same as the multiset of prime indices of n. For example, the prime indices of 12 are {1,1,2}, while a multiset whose multiplicities are {1,1,2} is {1,1,2,3}.
LINKS
EXAMPLE
The a(22) = 24 matrices:
[111112] [111121] [111211] [112111] [121111] [211111]
.
[111] [111] [111] [112] [121] [211]
[112] [121] [211] [111] [111] [111]
.
[11] [11] [11] [11] [12] [21]
[11] [11] [12] [21] [11] [11]
[12] [21] [11] [11] [11] [11]
.
[1] [1] [1] [1] [1] [2]
[1] [1] [1] [1] [2] [1]
[1] [1] [1] [2] [1] [1]
[1] [1] [2] [1] [1] [1]
[1] [2] [1] [1] [1] [1]
[2] [1] [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]]}]];
ptnmats[n_]:=Union@@Permutations/@Select[Union@@(Tuples[Permutations/@#]&/@Map[primeMS, facs[n], {2}]), SameQ@@Length/@#&];
nrmptn[n_]:=Join@@MapIndexed[Table[#2[[1]], {#1}]&, If[n==1, {}, Flatten[Cases[FactorInteger[n]//Reverse, {p_, k_}:>Table[PrimePi[p], {k}]]]]];
Array[Length[ptnmats[Times@@Prime/@nrmptn[#]]]&, 30]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 13 2019
STATUS
approved