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A325031 Numbers divisible by all prime indices of their prime indices. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A070932 A161577 A093686 * A155763 A030319 A226381

Adjacent sequences:  A325028 A325029 A325030 * A325032 A325033 A325034

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 25 2019

STATUS

approved

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Last modified April 3 01:31 EDT 2020. Contains 333195 sequences. (Running on oeis4.)