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%I #5 Jul 29 2019 13:55:37
%S 1,2,3,4,5,7,8,9,11,13,16,17,19,23,25,27,28,29,31,32,37,40,41,43,47,
%T 49,53,59,61,64,67,71,73,78,79,81,83,84,89,97,101,103,107,109,113,121,
%U 125,127,128,131,137,139,149,151,157,163,167,169,171,173,179,181
%N Heinz numbers of integer partitions of m >= 0 whose length times maximum is a multiple of m.
%C The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%C The enumeration of these partitions by sum is given by A326849.
%e The sequence of terms together with their prime indices begins:
%e 1: {}
%e 2: {1}
%e 3: {2}
%e 4: {1,1}
%e 5: {3}
%e 7: {4}
%e 8: {1,1,1}
%e 9: {2,2}
%e 11: {5}
%e 13: {6}
%e 16: {1,1,1,1}
%e 17: {7}
%e 19: {8}
%e 23: {9}
%e 25: {3,3}
%e 27: {2,2,2}
%e 28: {1,1,4}
%e 29: {10}
%e 31: {11}
%e 32: {1,1,1,1,1}
%e 37: {12}
%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t Select[Range[100],#==1||Divisible[Max[primeMS[#]]*Length[primeMS[#]],Total[primeMS[#]]]&]
%Y Cf. A001222, A047993, A056239, A061395, A067538, A112798, A316413, A326836, A326843, A326847, A326849, A326851.
%K nonn
%O 1,2
%A _Gus Wiseman_, Jul 26 2019
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