A325031 Numbers divisible by all prime indices of their prime indices.

1, 2, 3, 4, 6, 7, 8, 9, 10, 12, 14, 16, 18, 19, 20, 21, 24, 26, 27, 28, 30, 32, 33, 36, 38, 40, 42, 46, 48, 49, 50, 52, 53, 54, 56, 57, 60, 63, 64, 66, 68, 70, 72, 74, 76, 78, 80, 81, 84, 87, 90, 92, 96, 98, 99, 100, 104, 106, 108, 112, 114, 120, 122, 126, 128

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 does not belong to the sequence.

Links

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

Example

The sequence of multisets of multisets whose MM-numbers (see A302242) belong to the sequence begins:
   1: {}
   2: {{}}
   3: {{1}}
   4: {{},{}}
   6: {{},{1}}
   7: {{1,1}}
   8: {{},{},{}}
   9: {{1},{1}}
  10: {{},{2}}
  12: {{},{},{1}}
  14: {{},{1,1}}
  16: {{},{},{},{}}
  18: {{},{1},{1}}
  19: {{1,1,1}}
  20: {{},{},{2}}
  21: {{1},{1,1}}
  24: {{},{},{},{1}}
  26: {{},{1,2}}
  27: {{1},{1},{1}}
  28: {{},{},{1,1}}
  30: {{},{1},{2}}
  32: {{},{},{},{},{}}
  33: {{1},{3}}
  36: {{},{},{1},{1}}

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. A000720, A003963, A112798, A120383, A302242, A320325.

Cf. A323440, A324846, A324847, A324849, A324850, A324856, A324926, A325032.

Sequence in context: A161577 A358330 A093686 * A364433 A155763 A347350

Adjacent sequences: A325028 A325029 A325030 * A325032 A325033 A325034

Keyword

nonn

Author

Gus Wiseman, Mar 25 2019

Status

approved