cp's OEIS Frontend

A324696 Lexicographically earliest sequence containing 1 and all numbers divisible by prime(m) for some m not already in the sequence.

%I A324696 #6 Mar 11 2019 09:36:55
%S A324696 1,3,6,7,9,11,12,14,15,18,19,21,22,24,27,28,29,30,33,35,36,38,39,41,
%T A324696 42,44,45,48,49,51,53,54,55,56,57,58,59,60,63,66,69,70,71,72,75,76,77,
%U A324696 78,81,82,83,84,87,88,90,91,93,95,96,97,98,99,101,102,105
%N A324696 Lexicographically earliest sequence containing 1 and all numbers divisible by prime(m) for some m not already in the sequence.
%C A324696 A self-describing sequence, similar to A304360.
%C A324696 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 A324696 The sequence of terms together with their prime indices begins:
%e A324696    1: {}
%e A324696    3: {2}
%e A324696    6: {1,2}
%e A324696    7: {4}
%e A324696    9: {2,2}
%e A324696   11: {5}
%e A324696   12: {1,1,2}
%e A324696   14: {1,4}
%e A324696   15: {2,3}
%e A324696   18: {1,2,2}
%e A324696   19: {8}
%e A324696   21: {2,4}
%e A324696   22: {1,5}
%e A324696   24: {1,1,1,2}
%e A324696   27: {2,2,2}
%e A324696   28: {1,1,4}
%e A324696   29: {10}
%e A324696   30: {1,2,3}
%e A324696   33: {2,5}
%e A324696   35: {3,4}
%e A324696   36: {1,1,2,2}
%t A324696 aQ[n_]:=n==1||Or@@Cases[FactorInteger[n],{p_,k_}:>!aQ[PrimePi[p]]];
%t A324696 Select[Range[100],aQ]
%Y A324696 Complement of A304360.
%Y A324696 Cf. A000002, A000720, A001222, A001462, A007097, A055396, A061395, A079000, A079254, A109298, A112798, A276625, A277098.
%Y A324696 Cf. A324694, A324695, A324697, A324698, A324699, A324700, A324701, A324702, A324703, A324704, A324705.
%K A324696 nonn
%O A324696 1,2
%A A324696 _Gus Wiseman_, Mar 10 2019