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A327473 Heinz numbers of integer partitions whose mean A326567/A326568 is a part.

%I A327473 #5 Sep 13 2019 17:04:29
%S A327473 2,3,4,5,7,8,9,11,13,16,17,19,23,25,27,29,30,31,32,37,41,43,47,49,53,
%T A327473 59,61,64,67,71,73,79,81,83,84,89,90,97,101,103,105,107,109,110,113,
%U A327473 121,125,127,128,131,137,139,149,151,157,163,167,169,173,179,181
%N A327473 Heinz numbers of integer partitions whose mean A326567/A326568 is a part.
%C A327473 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%e A327473 The sequence of terms together with their prime indices begins:
%e A327473    2: {1}
%e A327473    3: {2}
%e A327473    4: {1,1}
%e A327473    5: {3}
%e A327473    7: {4}
%e A327473    8: {1,1,1}
%e A327473    9: {2,2}
%e A327473   11: {5}
%e A327473   13: {6}
%e A327473   16: {1,1,1,1}
%e A327473   17: {7}
%e A327473   19: {8}
%e A327473   23: {9}
%e A327473   25: {3,3}
%e A327473   27: {2,2,2}
%e A327473   29: {10}
%e A327473   30: {1,2,3}
%e A327473   31: {11}
%e A327473   32: {1,1,1,1,1}
%e A327473   37: {12}
%t A327473 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A327473 Select[Range[100],MemberQ[primeMS[#],Mean[primeMS[#]]]&]
%Y A327473 A subsequence of A316413.
%Y A327473 Complement of A327476.
%Y A327473 The enumeration of these partitions by sum is given by A237984.
%Y A327473 Subsets whose mean is a part are A065795.
%Y A327473 Numbers whose binary indices include their mean are A327478.
%Y A327473 Cf. A000016, A056239, A067538, A112798, A240850, A325706, A326567/A326568.
%K A327473 nonn
%O A327473 1,1
%A A327473 _Gus Wiseman_, Sep 13 2019