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

Author

Gus Wiseman, Mar 21 2019

Keywords

• nonn

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.

Examples

			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: {{},{},{},{},{},{}}
		

Links

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

Crossrefs

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

Programs

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[#]}]&]