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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 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 October 16 01:42 EDT 2019. Contains 328038 sequences. (Running on oeis4.)