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A325708 Numbers n whose prime indices cover an initial interval of positive integers and include all prime exponents of n.

%I A325708 #6 May 19 2019 06:17:49
%S A325708 1,2,6,12,18,30,36,60,90,120,150,180,210,270,300,360,420,450,540,600,
%T A325708 630,750,840,900,1050,1080,1260,1350,1470,1500,1680,1800,1890,2100,
%U A325708 2250,2310,2520,2700,2940,3000,3150,3780,4200,4410,4500,4620,5040,5250,5400
%N A325708 Numbers n whose prime indices cover an initial interval of positive integers and include all prime exponents of n.
%C A325708 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 covering an initial interval of positive integers and containing all of their distinct multiplicities. The enumeration of these partitions by sum is given by A325707.
%e A325708 The sequence of terms together with their prime indices begins:
%e A325708      1: {}
%e A325708      2: {1}
%e A325708      6: {1,2}
%e A325708     12: {1,1,2}
%e A325708     18: {1,2,2}
%e A325708     30: {1,2,3}
%e A325708     36: {1,1,2,2}
%e A325708     60: {1,1,2,3}
%e A325708     90: {1,2,2,3}
%e A325708    120: {1,1,1,2,3}
%e A325708    150: {1,2,3,3}
%e A325708    180: {1,1,2,2,3}
%e A325708    210: {1,2,3,4}
%e A325708    270: {1,2,2,2,3}
%e A325708    300: {1,1,2,3,3}
%e A325708    360: {1,1,1,2,2,3}
%e A325708    420: {1,1,2,3,4}
%e A325708    450: {1,2,2,3,3}
%e A325708    540: {1,1,2,2,2,3}
%e A325708    600: {1,1,1,2,3,3}
%t A325708 Select[Range[1000],#==1||Range[PrimeNu[#]]==PrimePi/@First/@FactorInteger[#]&&SubsetQ[PrimePi/@First/@FactorInteger[#],Last/@FactorInteger[#]]&]
%Y A325708 Cf. A055932, A109297, A114639, A114640, A181819, A290689, A290822, A325705, A325706, A325707.
%K A325708 nonn
%O A325708 1,2
%A A325708 _Gus Wiseman_, May 18 2019