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%I #6 Nov 18 2019 22:11:00
%S 1,2,3,5,7,9,11,13,17,19,23,25,27,29,31,37,41,43,47,49,53,59,61,67,71,
%T 73,79,81,83,89,91,97,101,103,107,109,113,121,125,127,131,137,139,149,
%U 151,157,163,167,169,173,179,181,191,193,197,199,203,211,223,227
%N MM-numbers of multiset clutters (connected weak antichains of multisets).
%C A weak antichain of multisets is a multiset of multisets, none of which is a proper subset of any other.
%F Equals {1} followed by the intersection of A305078 and A316476.
%e The sequence of terms tother with their corresponding clutters begins:
%e 1: {} 37: {{1,1,2}} 91: {{1,1},{1,2}}
%e 2: {{}} 41: {{6}} 97: {{3,3}}
%e 3: {{1}} 43: {{1,4}} 101: {{1,6}}
%e 5: {{2}} 47: {{2,3}} 103: {{2,2,2}}
%e 7: {{1,1}} 49: {{1,1},{1,1}} 107: {{1,1,4}}
%e 9: {{1},{1}} 53: {{1,1,1,1}} 109: {{10}}
%e 11: {{3}} 59: {{7}} 113: {{1,2,3}}
%e 13: {{1,2}} 61: {{1,2,2}} 121: {{3},{3}}
%e 17: {{4}} 67: {{8}} 125: {{2},{2},{2}}
%e 19: {{1,1,1}} 71: {{1,1,3}} 127: {{11}}
%e 23: {{2,2}} 73: {{2,4}} 131: {{1,1,1,1,1}}
%e 25: {{2},{2}} 79: {{1,5}} 137: {{2,5}}
%e 27: {{1},{1},{1}} 81: {{1},{1},{1},{1}} 139: {{1,7}}
%e 29: {{1,3}} 83: {{9}} 149: {{3,4}}
%e 31: {{5}} 89: {{1,1,1,2}} 151: {{1,1,2,2}}
%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t zsm[s_]:=With[{c=Select[Tuples[Range[Length[s]],2],And[Less@@#,GCD@@s[[#]]]>1&]},If[c=={},s,zsm[Sort[Append[Delete[s,List/@c[[1]]],LCM@@s[[c[[1]]]]]]]]];
%t stableQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];
%t Select[Range[100],And[stableQ[primeMS[#],Divisible],Length[zsm[primeMS[#]]]<=1]&]
%Y Connected numbers are A305078.
%Y Stable numbers are A316476.
%Y Clutters (of sets) are A048143.
%Y Cf. A056239, A112798, A289509, A302242, A302494, A304716, A318991, A319837, A320275, A320456, A328514, A329553, A329555.
%K nonn
%O 1,2
%A _Gus Wiseman_, Nov 18 2019