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A327476 Heinz numbers of integer partitions whose mean A326567/A326568 is not a part.

%I A327476 #4 Sep 13 2019 17:04:49
%S A327476 1,6,10,12,14,15,18,20,21,22,24,26,28,33,34,35,36,38,39,40,42,44,45,
%T A327476 46,48,50,51,52,54,55,56,57,58,60,62,63,65,66,68,69,70,72,74,75,76,77,
%U A327476 78,80,82,85,86,87,88,91,92,93,94,95,96,98,99,100,102,104,106
%N A327476 Heinz numbers of integer partitions whose mean A326567/A326568 is not a part.
%C A327476 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%e A327476 The sequence of terms together with their prime indices begins:
%e A327476     1: {}
%e A327476     6: {1,2}
%e A327476    10: {1,3}
%e A327476    12: {1,1,2}
%e A327476    14: {1,4}
%e A327476    15: {2,3}
%e A327476    18: {1,2,2}
%e A327476    20: {1,1,3}
%e A327476    21: {2,4}
%e A327476    22: {1,5}
%e A327476    24: {1,1,1,2}
%e A327476    26: {1,6}
%e A327476    28: {1,1,4}
%e A327476    33: {2,5}
%e A327476    34: {1,7}
%e A327476    35: {3,4}
%e A327476    36: {1,1,2,2}
%e A327476    38: {1,8}
%e A327476    39: {2,6}
%e A327476    40: {1,1,1,3}
%t A327476 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A327476 Select[Range[100],!MemberQ[primeMS[#],Mean[primeMS[#]]]&]
%Y A327476 Complement of A327473.
%Y A327476 The enumeration of these partitions by sum is given by A327472.
%Y A327476 Subsets whose mean is not an element are A327471.
%Y A327476 Cf. A056239, A067538, A112798, A114639, A237984, A240851, A316413, A324756, A324758, A326567/A326568, A327477.
%K A327476 nonn
%O A327476 1,2
%A A327476 _Gus Wiseman_, Sep 13 2019