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A325238 First positive integer with each omega-sequence. 21
1, 2, 4, 6, 8, 12, 16, 24, 30, 32, 36, 48, 60, 64, 96, 120, 128, 192, 210, 216, 240, 256, 360, 384, 420, 480, 512, 720, 768, 840, 900, 960, 1024, 1260, 1296, 1440, 1536, 1680, 1920, 2048, 2310, 2520, 2880, 3072, 3360, 3840, 4096, 4620, 5040, 5760, 6144, 6720 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

We define the omega-sequence of n (row n of A323023) to have length A323014(n) = frequency depth of n, and the k-th part is Omega(red^{k-1}(n)), where Omega = A001222 and red^{k} is the k-th functional iteration of red = A181819, given by red(n = p^i*...*q^j) = prime(i)*...*prime(j), i.e., the product of primes indexed by the prime exponents of n.

LINKS

Table of n, a(n) for n=1..52.

EXAMPLE

The sequence of terms together with their omega-sequences begins:

    1:

    2: 1

    4: 2 1

    6: 2 2 1

    8: 3 1

   12: 3 2 2 1

   16: 4 1

   24: 4 2 2 1

   30: 3 3 1

   32: 5 1

   36: 4 2 1

   48: 5 2 2 1

   60: 4 3 2 2 1

   64: 6 1

   96: 6 2 2 1

  120: 5 3 2 2 1

  128: 7 1

  192: 7 2 2 1

  210: 4 4 1

  216: 6 2 1

  240: 6 3 2 2 1

  256: 8 1

  360: 6 3 3 1

  384: 8 2 2 1

  420: 5 4 2 2 1

MATHEMATICA

tomseq[n_]:=If[n<=1, {}, Most[FixedPointList[Sort[Length/@Split[#]]&, Sort[Last/@FactorInteger[n]]]]];

omseqs=Table[Total/@tomseq[n], {n, 1000}];

Sort[Table[Position[omseqs, x][[1, 1]], {x, Union[omseqs]}]]

CROSSREFS

Cf. A001221, A001222, A007916, A011784, A070175, A071625, A118914, A181819, A181821, A303555, A304465, A323014, A323023, A325238, A325239.

Sequence in context: A095810 A025487 A279537 * A070175 A096850 A250270

Adjacent sequences:  A325235 A325236 A325237 * A325239 A325240 A325241

KEYWORD

nonn

AUTHOR

Gus Wiseman, Apr 14 2019

STATUS

approved

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Last modified September 16 08:53 EDT 2019. Contains 327092 sequences. (Running on oeis4.)