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A324705 Lexicographically earliest sequence containing 1 and all composite numbers divisible by prime(m) for some m already in the sequence.

%I A324705 #6 Mar 11 2019 20:49:06
%S A324705 1,4,6,8,10,12,14,16,18,20,21,22,24,26,28,30,32,34,35,36,38,39,40,42,
%T A324705 44,46,48,49,50,52,54,56,57,58,60,62,63,64,65,66,68,70,72,74,76,77,78,
%U A324705 80,82,84,86,87,88,90,91,92,94,95,96,98,100,102,104,105,106
%N A324705 Lexicographically earliest sequence containing 1 and all composite numbers divisible by prime(m) for some m already in the sequence.
%C A324705 A self-describing sequence, similar to A304360.
%C A324705 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.
%e A324705 The sequence of terms together with their prime indices begins:
%e A324705    1: {}
%e A324705    4: {1,1}
%e A324705    6: {1,2}
%e A324705    8: {1,1,1}
%e A324705   10: {1,3}
%e A324705   12: {1,1,2}
%e A324705   14: {1,4}
%e A324705   16: {1,1,1,1}
%e A324705   18: {1,2,2}
%e A324705   20: {1,1,3}
%e A324705   21: {2,4}
%e A324705   22: {1,5}
%e A324705   24: {1,1,1,2}
%e A324705   26: {1,6}
%e A324705   28: {1,1,4}
%e A324705   30: {1,2,3}
%e A324705   32: {1,1,1,1,1}
%e A324705   34: {1,7}
%e A324705   35: {3,4}
%e A324705   36: {1,1,2,2}
%t A324705 aQ[n_]:=Switch[n,1,True,_?PrimeQ,False,_,!And@@Cases[FactorInteger[n],{p_,k_}:>!aQ[PrimePi[p]]]];
%t A324705 Select[Range[200],aQ]
%Y A324705 Complement of A324697.
%Y A324705 Cf. A000002, A000720, A001222, A001462, A007097, A055396, A061395, A079000, A079254, A109298, A112798, A276625, A277098, A304360.
%Y A324705 Cf. A324694, A324695, A324696, A324698, A324699, A324700, A324701, A324702, A324703, A324704.
%K A324705 nonn
%O A324705 1,2
%A A324705 _Gus Wiseman_, Mar 11 2019