A324694 Lexicographically earliest sequence of positive integers divisible by prime(m) for some m not already in the sequence.

2, 4, 5, 6, 8, 10, 12, 14, 15, 16, 17, 18, 20, 22, 23, 24, 25, 26, 28, 30, 31, 32, 34, 35, 36, 38, 40, 41, 42, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 58, 60, 62, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 78, 80, 82, 84, 85, 86, 88, 90, 92, 93, 94, 95

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:
   2: {1}
   4: {1,1}
   5: {3}
   6: {1,2}
   8: {1,1,1}
  10: {1,3}
  12: {1,1,2}
  14: {1,4}
  15: {2,3}
  16: {1,1,1,1}
  17: {7}
  18: {1,2,2}
  20: {1,1,3}
  22: {1,5}
  23: {9}
  24: {1,1,1,2}
  25: {3,3}
  26: {1,6}
  28: {1,1,4}
  30: {1,2,3}
		

Crossrefs

Complement of A324695.

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

Cf. A324696, A324697, A324698, A324699, A324700, A324701, A324702, A324703, A324704, A324705.

Programs

Mathematica

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