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A325284 Numbers whose prime indices form an initial interval with a single hole: (1, 2, ..., x, x + 2, ..., m - 1, m), where x can be 0 but must be less than m - 1.

%I A325284 #7 Apr 19 2019 18:36:21
%S A325284 3,9,10,15,20,27,40,42,45,50,70,75,80,81,84,100,105,126,135,140,160,
%T A325284 168,200,225,243,250,252,280,294,315,320,330,336,350,375,378,400,405,
%U A325284 462,490,500,504,525,560,588,640,660,672,675,700,729,735,756,770,800
%N A325284 Numbers whose prime indices form an initial interval with a single hole: (1, 2, ..., x, x + 2, ..., m - 1, m), where x can be 0 but must be less than m - 1.
%C A325284 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%C A325284 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 whose distinct parts form an initial interval with a single hole. The enumeration of these partitions by sum is given by A090858.
%e A325284 The sequence of terms together with their prime indices begins:
%e A325284     3: {2}
%e A325284     9: {2,2}
%e A325284    10: {1,3}
%e A325284    15: {2,3}
%e A325284    20: {1,1,3}
%e A325284    27: {2,2,2}
%e A325284    40: {1,1,1,3}
%e A325284    42: {1,2,4}
%e A325284    45: {2,2,3}
%e A325284    50: {1,3,3}
%e A325284    70: {1,3,4}
%e A325284    75: {2,3,3}
%e A325284    80: {1,1,1,1,3}
%e A325284    81: {2,2,2,2}
%e A325284    84: {1,1,2,4}
%e A325284   100: {1,1,3,3}
%e A325284   105: {2,3,4}
%e A325284   126: {1,2,2,4}
%e A325284   135: {2,2,2,3}
%e A325284   140: {1,1,3,4}
%t A325284 Select[Range[100],Length[Complement[Range[PrimePi[FactorInteger[#][[-1,1]]]],PrimePi/@First/@FactorInteger[#]]]==1&]
%Y A325284 Cf. A055932, A056239, A061395, A090858, A112798, A124010, A127002, A130091, A325241, A325251, A325259, A325270.
%K A325284 nonn
%O A325284 1,1
%A A325284 _Gus Wiseman_, Apr 19 2019