A324324 - OEIS

%I #6 Feb 22 2019 21:16:29

%S 2117,3973,4843,5891,6757,7181,7801,10019,10063,11051,11567,13021,

%T 13193,13459,14123,14921,17603,18407,18761,18877,19307,19633,20941,

%U 21083,21251,21457,22849,23519,23533,24727,26101,27133,27169,27173,27413,29111,30479,31261

%N MM-numbers of crossing set partitions.

%C A multiset multisystem is a finite multiset of finite multisets. A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. The multiset multisystem with MM-number n is formed by taking the multiset of prime indices of each part in the multiset of prime indices of n. For example, the prime indices of 78 are {1,2,6}, so the multiset multisystem with MM-number 78 is {{},{1},{1,2}}.

%C A multiset multisystem is crossing if it contains two parts of the form {{...x...y...},{...z...t...}} with x < z < y < t or z < x < t < y.

%t croXQ[stn_]:=MatchQ[stn,{___,{___,x_,___,y_,___},___,{___,z_,___,t_,___},___}/;x<z<y<t||z<x<t<y];

%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];

%t setptnQ[bks_]:=UnsameQ@@Join@@bks&&!MemberQ[bks,{}];

%t Select[Range[10000],And[croXQ[primeMS/@primeMS[#]],setptnQ[primeMS/@primeMS[#]]]&]

%Y Cf. A000108 (non-crossing set partitions), A001055, A001222, A003963, A005117, A016098 (crossing set partitions), A054726, A056239, A112798, A302242, A302243, A302505, A302521 (MM-numbers of set partitions).

%Y Cf. A324166, A324167, A324169, A324170, A324171, A324326.

%K nonn

%O 1,1

%A _Gus Wiseman_, Feb 22 2019