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A325326 Heinz numbers of integer partitions covering an initial interval of positive integers with distinct multiplicities.

%I A325326 #4 May 02 2019 08:52:39
%S A325326 1,2,4,8,12,16,18,24,32,48,54,64,72,96,108,128,144,162,192,256,288,
%T A325326 324,360,384,432,486,512,540,576,600,648,720,768,864,972,1024,1152,
%U A325326 1200,1350,1440,1458,1500,1536,1620,1728,1944,2048,2160,2250,2304,2400,2592
%N A325326 Heinz numbers of integer partitions covering an initial interval of positive integers with distinct multiplicities.
%C A325326 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%C A325326 The enumeration of these partitions by sum is given by A320348.
%F A325326 Intersection of normal numbers (A055932) and numbers with distinct prime exponents (A130091).
%e A325326 The sequence of terms together with their prime indices begins:
%e A325326      1: {}
%e A325326      2: {1}
%e A325326      4: {1,1}
%e A325326      8: {1,1,1}
%e A325326     12: {1,1,2}
%e A325326     16: {1,1,1,1}
%e A325326     18: {1,2,2}
%e A325326     24: {1,1,1,2}
%e A325326     32: {1,1,1,1,1}
%e A325326     48: {1,1,1,1,2}
%e A325326     54: {1,2,2,2}
%e A325326     64: {1,1,1,1,1,1}
%e A325326     72: {1,1,1,2,2}
%e A325326     96: {1,1,1,1,1,2}
%e A325326    108: {1,1,2,2,2}
%e A325326    128: {1,1,1,1,1,1,1}
%e A325326    144: {1,1,1,1,2,2}
%e A325326    162: {1,2,2,2,2}
%e A325326    192: {1,1,1,1,1,1,2}
%e A325326    256: {1,1,1,1,1,1,1,1}
%e A325326    288: {1,1,1,1,1,2,2}
%e A325326    324: {1,1,2,2,2,2}
%e A325326    360: {1,1,1,2,2,3}
%e A325326    384: {1,1,1,1,1,1,1,2}
%t A325326 normQ[n_Integer]:=n==1||PrimePi/@First/@FactorInteger[n]==Range[PrimeNu[n]];
%t A325326 Select[Range[100],normQ[#]&&UnsameQ@@Last/@FactorInteger[#]&]
%Y A325326 Cf. A000837, A047966, A055932, A056239, A098859, A112798, A130091, A317081, A317089, A320348, A325329, A325337, A325369, A325372.
%K A325326 nonn
%O A325326 1,2
%A A325326 _Gus Wiseman_, May 01 2019