A320324 Numbers of which each prime index has the same number of prime factors, counted with multiplicity.

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

Offset

1,2

Comments

A prime index of n is a number m such that prime(m) divides n.

Links

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

Gus Wiseman, Sequences counting and ranking multiset partitions whose part lengths, sums, or averages are constant or strict.

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. A001222, A038041, A112798, A302242, A306017, A317583, A319066, A319169, A320325, A322794, A326533, A326534, A326535, A326536, A326537.

Sequence in context: A328674 A316476 A056867 * A321698 A325394 A358378

Adjacent sequences: A320321 A320322 A320323 * A320325 A320326 A320327

Keyword

nonn

Author

Gus Wiseman, Oct 10 2018

Status

approved