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A304450 Numbers that are not perfect powers and whose prime factors span an initial interval of prime numbers.

%I A304450 #9 Aug 26 2018 18:40:43
%S A304450 2,6,12,18,24,30,48,54,60,72,90,96,108,120,150,162,180,192,210,240,
%T A304450 270,288,300,360,384,420,432,450,480,486,540,600,630,648,720,750,768,
%U A304450 810,840,864,960,972,1050,1080,1152,1200,1260,1350,1440,1458,1470,1500,1536
%N A304450 Numbers that are not perfect powers and whose prime factors span an initial interval of prime numbers.
%C A304450 The multiset of prime indices of a(n) is the a(n)-th row of A112798. This multiset is normal, meaning it spans an initial interval of positive integers, and aperiodic, meaning its multiplicities are relatively prime.
%H A304450 Andrew Howroyd, <a href="/A304450/b304450.txt">Table of n, a(n) for n = 1..1000</a>
%F A304450 Intersection of A007916 and A055932.
%e A304450 Sequence of all normal aperiodic multisets begins
%e A304450 2:   {1}
%e A304450 6:   {1,2}
%e A304450 12:  {1,1,2}
%e A304450 18:  {1,2,2}
%e A304450 24:  {1,1,1,2}
%e A304450 30:  {1,2,3}
%e A304450 48:  {1,1,1,1,2}
%e A304450 54:  {1,2,2,2}
%e A304450 60:  {1,1,2,3}
%e A304450 72:  {1,1,1,2,2}
%e A304450 90:  {1,2,2,3}
%e A304450 96:  {1,1,1,1,1,2}
%e A304450 108: {1,1,2,2,2}
%e A304450 120: {1,1,1,2,3}
%e A304450 150: {1,2,3,3}
%e A304450 162: {1,2,2,2,2}
%e A304450 180: {1,1,2,2,3}
%e A304450 192: {1,1,1,1,1,1,2}
%e A304450 210: {1,2,3,4}
%e A304450 240: {1,1,1,1,2,3}
%e A304450 270: {1,2,2,2,3}
%e A304450 288: {1,1,1,1,1,2,2}
%e A304450 300: {1,1,2,3,3}
%e A304450 360: {1,1,1,2,2,3}
%e A304450 384: {1,1,1,1,1,1,1,2}
%t A304450 Select[Range[1000],FactorInteger[#][[-1,1]]==Prime[Length[FactorInteger[#]]]&&GCD@@FactorInteger[#][[All,2]]===1&]
%o A304450 (PARI) ok(n)={my(f=factor(n)[,1]); #f && !ispower(n) && #f==primepi(f[#f])} \\ _Andrew Howroyd_, Aug 26 2018
%Y A304450 Cf. A000005, A000740, A000837, A000961, A001597, A001694, A005117, A007916, A052409, A052410, A055932, A056239, A112798, A303431, A303546, A303945.
%K A304450 nonn
%O A304450 1,1
%A A304450 _Gus Wiseman_, May 12 2018