cp's OEIS Frontend

A322454 Number of multiset partitions with no constant parts of a multiset whose multiplicities are the prime indices of n.

%I A322454 #4 Dec 09 2018 12:28:57
%S A322454 1,0,0,1,0,1,0,1,2,1,0,2,0,1,2,4,0,4,0,3,3,1,0,7,4,1,9,4,0,7,0,11,3,1,
%T A322454 5,15,0,1,4,11
%N A322454 Number of multiset partitions with no constant parts of a multiset whose multiplicities are the prime indices of n.
%C A322454 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}.
%e A322454 The a(30) = 7 multiset partitions:
%e A322454     {{1,1,1,2,2,3}}
%e A322454    {{1,2},{1,1,2,3}}
%e A322454    {{1,3},{1,1,2,2}}
%e A322454    {{2,3},{1,1,1,2}}
%e A322454    {{1,1,2},{1,2,3}}
%e A322454    {{1,1,3},{1,2,2}}
%e A322454   {{1,2},{1,2},{1,3}}
%t A322454 nrmptn[n_]:=Join@@MapIndexed[Table[#2[[1]],{#1}]&,If[n==1,{},Flatten[Cases[FactorInteger[n]//Reverse,{p_,k_}:>Table[PrimePi[p],{k}]]]]];
%t A322454 sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t A322454 mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];
%t A322454 Table[Length[Select[mps[nrmptn[n]],Min@@Length/@Union/@#>1&]],{n,20}]
%Y A322454 Cf. A000688, A000961, A001055, A001597, A023893, A023894, A181821, A318284, A320322, A321407, A321760, A322260, A322452.
%K A322454 nonn,more
%O A322454 1,9
%A A322454 _Gus Wiseman_, Dec 09 2018