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%I #4 Sep 13 2019 17:04:49
%S 1,6,10,12,14,15,18,20,21,22,24,26,28,33,34,35,36,38,39,40,42,44,45,
%T 46,48,50,51,52,54,55,56,57,58,60,62,63,65,66,68,69,70,72,74,75,76,77,
%U 78,80,82,85,86,87,88,91,92,93,94,95,96,98,99,100,102,104,106
%N Heinz numbers of integer partitions whose mean A326567/A326568 is not a part.
%C The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%e The sequence of terms together with their prime indices begins:
%e 1: {}
%e 6: {1,2}
%e 10: {1,3}
%e 12: {1,1,2}
%e 14: {1,4}
%e 15: {2,3}
%e 18: {1,2,2}
%e 20: {1,1,3}
%e 21: {2,4}
%e 22: {1,5}
%e 24: {1,1,1,2}
%e 26: {1,6}
%e 28: {1,1,4}
%e 33: {2,5}
%e 34: {1,7}
%e 35: {3,4}
%e 36: {1,1,2,2}
%e 38: {1,8}
%e 39: {2,6}
%e 40: {1,1,1,3}
%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t Select[Range[100],!MemberQ[primeMS[#],Mean[primeMS[#]]]&]
%Y Complement of A327473.
%Y The enumeration of these partitions by sum is given by A327472.
%Y Subsets whose mean is not an element are A327471.
%Y Cf. A056239, A067538, A112798, A114639, A237984, A240851, A316413, A324756, A324758, A326567/A326568, A327477.
%K nonn
%O 1,2
%A _Gus Wiseman_, Sep 13 2019
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