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A320324 Numbers of which each prime index has the same number of prime factors, counted with multiplicity. 9
1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 15, 16, 17, 19, 23, 25, 27, 29, 31, 32, 33, 37, 41, 43, 45, 47, 49, 51, 53, 55, 59, 61, 64, 67, 71, 73, 75, 79, 81, 83, 85, 89, 91, 93, 97, 99, 101, 103, 107, 109, 113, 121, 123, 125, 127, 128, 131, 135, 137, 139, 149, 151, 153 (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.

LINKS

Table of n, a(n) for n=1..63.

EXAMPLE

The terms together with their corresponding multiset multisystems (A302242):

   1: {}

   2: {{}}

   3: {{1}}

   4: {{},{}}

   5: {{2}}

   7: {{1,1}}

   8: {{},{},{}}

   9: {{1},{1}}

  11: {{3}}

  13: {{1,2}}

  15: {{1},{2}}

  16: {{},{},{},{}}

  17: {{4}}

  19: {{1,1,1}}

  23: {{2,2}}

  25: {{2},{2}}

  27: {{1},{1},{1}}

  29: {{1,3}}

  31: {{5}}

  32: {{},{},{},{},{}}

  33: {{1},{3}}

  37: {{1,1,2}}

  41: {{6}}

  43: {{1,4}}

  45: {{1},{1},{2}}

  47: {{2,3}}

  49: {{1,1},{1,1}}

MATHEMATICA

Select[Range[100], SameQ@@PrimeOmega/@PrimePi/@First/@FactorInteger[#]&]

PROG

(PARI) is(n) = #Set(apply(p -> bigomega(primepi(p)), factor(n)[, 1]~))<=1 \\ Rémy Sigrist, Oct 11 2018

CROSSREFS

Cf. A000720, A001222, A003963, A056239, A064573, A112798, A302242, A305551, A306017, A319056, A319066, A319169, A320323, A320325.

Sequence in context: A257144 A316476 A056867 * A321698 A062491 A087092

Adjacent sequences:  A320321 A320322 A320323 * A320325 A320326 A320327

KEYWORD

nonn

AUTHOR

Gus Wiseman, Oct 10 2018

STATUS

approved

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Last modified March 23 02:41 EDT 2019. Contains 321422 sequences. (Running on oeis4.)