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A325277 Irregular triangle read by rows where row 1 is {1} and row n is the sequence starting with n and repeatedly applying A181819 until a prime number is reached. 34
1, 2, 3, 4, 3, 5, 6, 4, 3, 7, 8, 5, 9, 3, 10, 4, 3, 11, 12, 6, 4, 3, 13, 14, 4, 3, 15, 4, 3, 16, 7, 17, 18, 6, 4, 3, 19, 20, 6, 4, 3, 21, 4, 3, 22, 4, 3, 23, 24, 10, 4, 3, 25, 3, 26, 4, 3, 27, 5, 28, 6, 4, 3, 29, 30, 8, 5, 31, 32, 11, 33, 4, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The function A181819 maps p^i*...*q^j to prime(i)*...*prime(j) where p through q are distinct primes.

LINKS

Table of n, a(n) for n=1..73.

FORMULA

T(n,k) = A325239(n,k) for k <= A323014(n).

A001222(T(n,k)) = A323023(n,k) for n > 1.

EXAMPLE

Triangle begins:

   1            26 4 3        51 4 3          76 6 4 3

   2            27 5          52 6 4 3        77 4 3

   3            28 6 4 3      53              78 8 5

   4 3          29            54 10 4 3       79

   5            30 8 5        55 4 3          80 14 4 3

   6 4 3        31            56 10 4 3       81 7

   7            32 11         57 4 3          82 4 3

   8 5          33 4 3        58 4 3          83

   9 3          34 4 3        59              84 12 6 4 3

  10 4 3        35 4 3        60 12 6 4 3     85 4 3

  11            36 9 3        61              86 4 3

  12 6 4 3      37            62 4 3          87 4 3

  13            38 4 3        63 6 4 3        88 10 4 3

  14 4 3        39 4 3        64 13           89

  15 4 3        40 10 4 3     65 4 3          90 12 6 4 3

  16 7          41            66 8 5          91 4 3

  17            42 8 5        67              92 6 4 3

  18 6 4 3      43            68 6 4 3        93 4 3

  19            44 6 4 3      69 4 3          94 4 3

  20 6 4 3      45 6 4 3      70 8 5          95 4 3

  21 4 3        46 4 3        71              96 22 4 3

  22 4 3        47            72 15 4 3       97

  23            48 14 4 3     73              98 6 4 3

  24 10 4 3     49 3          74 4 3          99 6 4 3

  25 3          50 6 4 3      75 6 4 3       100 9 3

MATHEMATICA

red[n_]:=Times@@Prime/@Last/@If[n==1, {}, FactorInteger[n]];

Table[NestWhileList[red, n, #>1&&!PrimeQ[#]&], {n, 30}]

CROSSREFS

Row lengths are 1 for n = 1 and A323014(n) for n > 1.

Cf. A001221, A001222, A071625, A118914, A181819, A181821, A182850, A182857, A323022, A323023, A325238, A325239.

Sequence in context: A305747 A304736 A286448 * A257573 A182973 A278056

Adjacent sequences:  A325274 A325275 A325276 * A325278 A325279 A325280

KEYWORD

nonn,tabf

AUTHOR

Gus Wiseman, Apr 15 2019

STATUS

approved

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Last modified November 14 17:21 EST 2019. Contains 329126 sequences. (Running on oeis4.)