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A265668 Table read by rows: prime factors of squarefree numbers; a(1) = 1 by convention. 12

%I

%S 1,2,3,5,2,3,7,2,5,11,13,2,7,3,5,17,19,3,7,2,11,23,2,13,29,2,3,5,31,3,

%T 11,2,17,5,7,37,2,19,3,13,41,2,3,7,43,2,23,47,3,17,53,5,11,3,19,2,29,

%U 59,61,2,31,5,13,2,3,11,67,3,23,2,5,7,71,73,2

%N Table read by rows: prime factors of squarefree numbers; a(1) = 1 by convention.

%C For n > 1: A072047(n) = length of row n;

%C T(n,1) = A073481(n); T(n,A001221(n)) = A073482(n);

%C for n > 1: A111060(n) = sum of row n;

%C A005117(n) = product of row n.

%H Reinhard Zumkeller, <a href="/A265668/b265668.txt">Rows n = 1..1000 of triangle, flattened</a>

%e . n | T(n,*) A5117(n) n | T(n,*) A5117(n) n | T(n,*) A5117(n)

%e . ----+---------+------ ----+---------+------ ----+----------+------

%e . 1 | [1] | 1 21 | [3,11] | 33 41 | [2,3,11] | 66

%e . 2 | [2] | 2 22 | [2,17] | 34 42 | [67] | 67

%e . 3 | [3] | 3 23 | [5,7] | 35 43 | [3,23] | 69

%e . 4 | [5] | 5 24 | [37] | 37 44 | [2,5,7] | 70

%e . 5 | [2,3] | 6 25 | [2,19] | 38 45 | [71] | 71

%e . 6 | [7] | 7 26 | [3,13] | 39 46 | [73] | 73

%e . 7 | [2,5] | 10 27 | [41] | 41 47 | [2,37] | 74

%e . 8 | [11] | 11 28 | [2,3,7] | 42 48 | [7,11] | 77

%e . 9 | [13] | 13 29 | [43] | 43 49 | [2,3,13] | 78

%e . 10 | [2,7] | 14 30 | [2,23] | 46 50 | [79] | 79

%e . 11 | [3,5] | 15 31 | [47] | 47 51 | [2,41] | 82

%e . 12 | [17] | 17 32 | [3,17] | 51 52 | [83] | 83

%e . 13 | [19] | 19 33 | [53] | 53 53 | [5,17] | 85

%e . 14 | [3,7] | 21 34 | [5,11] | 55 54 | [2,43] | 86

%e . 15 | [2,11] | 22 35 | [3,19] | 57 55 | [3,29] | 87

%e . 16 | [23] | 23 36 | [2,29] | 58 56 | [89] | 89

%e . 17 | [2,13] | 26 37 | [59] | 59 57 | [7,13] | 91

%e . 18 | [29] | 29 38 | [61] | 61 58 | [3,31] | 93

%e . 19 | [2,3,5] | 30 39 | [2,31] | 62 59 | [2,47] | 94

%e . 20 | [31] | 31 40 | [5,13] | 65 60 | [5,19] | 95 .

%t FactorInteger[#][[All,1]]&/@Select[Range[100],SquareFreeQ]//Flatten (* _Harvey P. Dale_, Apr 27 2018 *)

%o (Haskell)

%o import Math.NumberTheory.Primes.Factorisation (factorise)

%o import Data.Maybe (mapMaybe)

%o a265668 n k = a265668_tabf !! (n-1) !! (k-1)

%o a265668_row n = a265668_tabf !! (n-1)

%o a265668_tabf = [1] : mapMaybe f [2..] where

%o f x = if all (== 1) es then Just ps else Nothing

%o where (ps, es) = unzip $ factorise x

%Y Cf. A005117, A027748, A124010, A072047 (row lengths), A073481, A073482, A001221, A111060, A049200, A062822.

%K nonn,tabf

%O 1,2

%A _Reinhard Zumkeller_, Dec 13 2015

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Last modified April 13 11:56 EDT 2021. Contains 342936 sequences. (Running on oeis4.)