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%I #8 Sep 19 2018 09:17:01
%S 165,255,385,465,561,595,615,759,885,935,1001,1005,1015,1023,1045,
%T 1085,1173,1245,1309,1353,1435,1455,1505,1547,1581,1615,1635,1705,
%U 1771,1905,1947,2065,2091,2139,2211,2235,2255,2345,2355,2365,2387,2397,2409,2431,2465
%N Heinz numbers of integer partitions such that not every distinct submultiset has a different GCD but every distinct submultiset has a different LCM.
%C The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%C The first term of this sequence absent from A302696 (numbers whose prime indices are pairwise coprime) is 1001 with prime indices {4,5,6}.
%e The sequence of partitions whose Heinz numbers belong to this sequence begins (5,3,2), (7,3,2), (5,4,3), (11,3,2), (7,5,2), (7,4,3), (13,3,2), (9,5,2), (17,3,2), (7,5,3).
%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t Select[Range[10000],UnsameQ@@primeMS[#]&&And[!UnsameQ@@GCD@@@Union[Rest[Subsets[primeMS[#]]]],UnsameQ@@LCM@@@Union[Rest[Subsets[primeMS[#]]]]]&]
%Y Cf. A056239, A275972, A299702, A301899, A301900, A319315, A319319, A319327.
%K nonn
%O 1,1
%A _Gus Wiseman_, Sep 17 2018
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