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

1, 3, 6, 7, 9, 11, 12, 14, 15, 18, 19, 21, 22, 24, 27, 28, 29, 30, 33, 35, 36, 38, 39, 41, 42, 44, 45, 48, 49, 51, 53, 54, 55, 56, 57, 58, 59, 60, 63, 66, 69, 70, 71, 72, 75, 76, 77, 78, 81, 82, 83, 84, 87, 88, 90, 91, 93, 95, 96, 97, 98, 99, 101, 102, 105

Offset: 1

Author

Gus Wiseman, Mar 10 2019

Keywords

• nonn

Comments

A self-describing sequence, similar to A304360.

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.

Examples

			The sequence of terms together with their prime indices begins:
   1: {}
   3: {2}
   6: {1,2}
   7: {4}
   9: {2,2}
  11: {5}
  12: {1,1,2}
  14: {1,4}
  15: {2,3}
  18: {1,2,2}
  19: {8}
  21: {2,4}
  22: {1,5}
  24: {1,1,1,2}
  27: {2,2,2}
  28: {1,1,4}
  29: {10}
  30: {1,2,3}
  33: {2,5}
  35: {3,4}
  36: {1,1,2,2}
		

Crossrefs

Complement of A304360.

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

Cf. A324694, A324695, A324697, A324698, A324699, A324700, A324701, A324702, A324703, A324704, A324705.

Programs

Mathematica

aQ[n_]:=n==1||Or@@Cases[FactorInteger[n],{p_,k_}:>!aQ[PrimePi[p]]];
Select[Range[100],aQ]