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A325781 Heinz numbers of complete integer partitions.

%I A325781 #4 May 22 2019 21:00:30
%S A325781 1,2,4,6,8,12,16,18,20,24,30,32,36,40,42,48,54,56,60,64,72,80,84,90,
%T A325781 96,100,108,112,120,126,128,132,140,144,150,160,162,168,176,180,192,
%U A325781 198,200,210,216,220,224,234,240,252,256,260,264,270,280,288,294,300
%N A325781 Heinz numbers of complete integer partitions.
%C A325781 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%C A325781 The sum of prime indices of n is A056239(n). A number is in this sequence iff its divisors have sums of prime indices covering an initial interval of nonnegative integers. For example, the divisors of 60 are {1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60}, with respective sums of prime indices {0, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 7}, so 60 is in the sequence.
%e A325781 The sequence of terms together with their prime indices begins:
%e A325781      1: {}
%e A325781      2: {1}
%e A325781      4: {1,1}
%e A325781      6: {1,2}
%e A325781      8: {1,1,1}
%e A325781     12: {1,1,2}
%e A325781     16: {1,1,1,1}
%e A325781     18: {1,2,2}
%e A325781     20: {1,1,3}
%e A325781     24: {1,1,1,2}
%e A325781     30: {1,2,3}
%e A325781     32: {1,1,1,1,1}
%e A325781     36: {1,1,2,2}
%e A325781     40: {1,1,1,3}
%e A325781     42: {1,2,4}
%e A325781     48: {1,1,1,1,2}
%e A325781     54: {1,2,2,2}
%e A325781     56: {1,1,1,4}
%e A325781     60: {1,1,2,3}
%e A325781     64: {1,1,1,1,1,1}
%t A325781 normQ[m_]:=Or[m=={},Union[m]==Range[Max[m]]];
%t A325781 hwt[n_]:=Total[Cases[FactorInteger[n],{p_,k_}:>PrimePi[p]*k]];
%t A325781 Select[Range[1000],normQ[hwt/@Rest[Divisors[#]]]&]
%Y A325781 Cf. A002033, A056239, A103295, A112798, A126796, A188431, A299702, A325684, A325770, A325780, A325782.
%K A325781 nonn
%O A325781 1,2
%A A325781 _Gus Wiseman_, May 21 2019