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

1,2

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.

Links

Table of n, a(n) for n=1..65.

Example

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}

Mathematica

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

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.

Sequence in context: A085837 A176237 A187811 * A186348 A071822 A268380

Adjacent sequences: A324693 A324694 A324695 * A324697 A324698 A324699

Keyword

nonn

Author

Gus Wiseman, Mar 10 2019

Status

approved