A324704 - OEIS

%I #4 Mar 11 2019 20:48:59

%S 1,4,6,7,8,10,12,13,14,16,17,18,19,20,21,22,24,26,28,29,30,32,34,35,

%T 36,37,38,39,40,41,42,43,44,46,48,49,50,51,52,53,54,56,57,58,59,60,61,

%U 62,63,64,65,66,67,68,70,71,72,73,74,76,77,78,79,80,82,84

%N Lexicographically earliest sequence containing 1 and all numbers > 2 divisible by prime(m) for some m already in the sequence.

%C A self-describing sequence, similar to A304360.

%C 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 The sequence of terms together with their prime indices begins:

%e    1: {}

%e    4: {1,1}

%e    6: {1,2}

%e    7: {4}

%e    8: {1,1,1}

%e   10: {1,3}

%e   12: {1,1,2}

%e   13: {6}

%e   14: {1,4}

%e   16: {1,1,1,1}

%e   17: {7}

%e   18: {1,2,2}

%e   19: {8}

%e   20: {1,1,3}

%e   21: {2,4}

%e   22: {1,5}

%e   24: {1,1,1,2}

%e   26: {1,6}

%e   28: {1,1,4}

%t aQ[n_]:=Switch[n,1,True,2,False,_,!And@@Cases[FactorInteger[n],{p_,k_}:>!aQ[PrimePi[p]]]];

%t Select[Range[100],aQ]

%Y Complement of A324698.

%Y Cf. A000002, A000720, A001222, A001462, A007097, A055396, A061395, A079000, A079254, A109298, A112798, A276625, A277098, A304360.

%Y Cf. A324694, A324695, A324696, A324697, A324699, A324700, A324701, A324702, A324703, A324705.

%K nonn

%O 1,2

%A _Gus Wiseman_, Mar 11 2019