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A325763 Heinz numbers of integer partitions whose consecutive subsequence-sums cover an initial interval of positive integers.

%I A325763 #6 May 19 2019 20:33:04
%S A325763 1,2,4,6,8,12,16,18,20,24,32,36,40,48,54,56,60,64,72,80,96,100,108,
%T A325763 112,120,128,144,160,162,168,176,180,192,200,216,224,240,256,280,288,
%U A325763 300,320,324,336,352,360,384,392,400,416,432,448,480,486,500,504,512
%N A325763 Heinz numbers of integer partitions whose consecutive subsequence-sums cover an initial interval of positive integers.
%C A325763 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%C A325763 The enumeration of these partitions by sum appears to be A002865.
%e A325763 The sequence of terms together with their prime indices begins:
%e A325763      1: {}
%e A325763      2: {1}
%e A325763      4: {1,1}
%e A325763      6: {1,2}
%e A325763      8: {1,1,1}
%e A325763     12: {1,1,2}
%e A325763     16: {1,1,1,1}
%e A325763     18: {1,2,2}
%e A325763     20: {1,1,3}
%e A325763     24: {1,1,1,2}
%e A325763     32: {1,1,1,1,1}
%e A325763     36: {1,1,2,2}
%e A325763     40: {1,1,1,3}
%e A325763     48: {1,1,1,1,2}
%e A325763     54: {1,2,2,2}
%e A325763     56: {1,1,1,4}
%e A325763     60: {1,1,2,3}
%e A325763     64: {1,1,1,1,1,1}
%e A325763     72: {1,1,1,2,2}
%e A325763     80: {1,1,1,1,3}
%t A325763 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A325763 Select[Range[100],Range[Total[primeMS[#]]]==Union[ReplaceList[primeMS[#],{___,s__,___}:>Plus[s]]]&]
%Y A325763 Cf. A002033, A103295, A103300, A169942, A325676, A325685, A325764, A325765.
%K A325763 nonn
%O A325763 1,2
%A A325763 _Gus Wiseman_, May 19 2019