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%I #6 Jan 14 2019 18:25:47
%S 6,10,12,14,15,18,20,21,22,24,26,28,30,33,34,35,38,39,40,42,44,45,46,
%T 48,50,51,52,54,55,56,57,58,60,62,63,65,66,68,69,70,72,74,75,76,77,78,
%U 80,82,84,85,86,87,88,90,91,92,93,94,95,96,98,99,102,104,105
%N Heinz numbers of integer partitions that cannot be arranged into a matrix with equal row-sums and equal column-sums.
%C The first term of this sequence absent from A106543 is 144.
%C The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%H <a href="/index/He#Heinz">Index entries for sequences related to Heinz numbers</a>
%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t ptnmats[n_]:=Union@@Permutations/@Select[Union@@(Tuples[Permutations/@#]&/@Map[primeMS,facs[n],{2}]),SameQ@@Length/@#&];
%t Select[Range[2,1000],Select[ptnmats[#],And[SameQ@@Total/@#,SameQ@@Total/@Transpose[#]]&]=={}&]
%Y Complement of A323306.
%Y Cf. A006052, A007016, A008480, A056239, A112798, A120733, A319056, A321719, A321721.
%Y Cf. A323300, A323302, A323305, A323347, A323348, A323349.
%K nonn
%O 1,1
%A _Gus Wiseman_, Jan 13 2019
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