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A325337 Numbers whose prime exponents are distinct and cover an initial interval of positive integers.

%I A325337 #5 May 02 2019 08:54:02
%S A325337 1,2,3,5,7,11,12,13,17,18,19,20,23,28,29,31,37,41,43,44,45,47,50,52,
%T A325337 53,59,61,63,67,68,71,73,75,76,79,83,89,92,97,98,99,101,103,107,109,
%U A325337 113,116,117,124,127,131,137,139,147,148,149,151,153,157,163,164
%N A325337 Numbers whose prime exponents are distinct and cover an initial interval of positive integers.
%C A325337 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are Heinz numbers of integer partitions with distinct multiplicities covering an initial interval of positive integers. The enumeration of these partitions by sum is given by A320348.
%e A325337 The sequence of terms together with their prime indices begins:
%e A325337    1: {}
%e A325337    2: {1}
%e A325337    3: {2}
%e A325337    5: {3}
%e A325337    7: {4}
%e A325337   11: {5}
%e A325337   12: {1,1,2}
%e A325337   13: {6}
%e A325337   17: {7}
%e A325337   18: {1,2,2}
%e A325337   19: {8}
%e A325337   20: {1,1,3}
%e A325337   23: {9}
%e A325337   28: {1,1,4}
%e A325337   29: {10}
%e A325337   31: {11}
%e A325337   37: {12}
%e A325337   41: {13}
%e A325337   43: {14}
%e A325337   44: {1,1,5}
%t A325337 normQ[m_]:=Or[m=={},Union[m]==Range[Max[m]]];
%t A325337 Select[Range[100],UnsameQ@@Last/@FactorInteger[#]&&normQ[Last/@FactorInteger[#]]&]
%Y A325337 Cf. A055932, A056239, A112798, A317081, A317089, A317090, A325326, A325330, A325370, A325371.
%K A325337 nonn
%O A325337 1,2
%A A325337 _Gus Wiseman_, May 01 2019