A324926 Numbers not divisible by any prime indices of their prime indices.

1, 2, 4, 5, 8, 11, 16, 17, 22, 23, 25, 31, 32, 34, 41, 44, 47, 55, 59, 62, 64, 67, 73, 82, 83, 85, 88, 97, 103, 109, 115, 118, 121, 124, 125, 127, 128, 134, 137, 149, 157, 164, 166, 167, 176, 179, 187, 191, 194, 197, 205, 211, 218, 227, 233, 235, 236, 241, 242

Offset

1,2

Comments

A prime index of n is a number m such that prime(m) divides n. For example, the prime indices of 55 are {3,5} with prime indices {{2},{3}}. Since 55 is not divisible by 2 or 3, it belongs to the sequence.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

The sequence of multisets of multisets whose MM-numbers (see A302242) belong to the sequence begins:
   1: {}
   2: {{}}
   4: {{},{}}
   5: {{2}}
   8: {{},{},{}}
  11: {{3}}
  16: {{},{},{},{}}
  17: {{4}}
  22: {{},{3}}
  23: {{2,2}}
  25: {{2},{2}}
  31: {{5}}
  32: {{},{},{},{},{}}
  34: {{},{4}}
  41: {{6}}
  44: {{},{},{3}}
  47: {{2,3}}
  55: {{2},{3}}
  59: {{7}}
  62: {{},{5}}
  64: {{},{},{},{},{},{}}

Mathematica

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], And@@Table[!Divisible[#, i], {i, Union@@primeMS/@primeMS[#]}]&]

Crossrefs

Cf. A001222, A003963, A112798, A120383, A302242, A304360, A324846, A324847, A324848, A324849, A324850, A324927, A324928, A324930.

Sequence in context: A222044 A288937 A327063 * A175106 A216566 A205728

Adjacent sequences: A324923 A324924 A324925 * A324927 A324928 A324929

Keyword

nonn

Author

Gus Wiseman, Mar 21 2019

Status

approved