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

%I A265668 #6 Apr 27 2018 10:38:27
%S A265668 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 A265668 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 A265668 59,61,2,31,5,13,2,3,11,67,3,23,2,5,7,71,73,2
%N A265668 Table read by rows: prime factors of squarefree numbers; a(1) = 1 by convention.
%C A265668 For n > 1: A072047(n) = length of row n;
%C A265668 T(n,1) = A073481(n); T(n,A001221(n)) = A073482(n);
%C A265668 for n > 1: A111060(n) = sum of row n;
%C A265668 A005117(n) = product of row n.
%H A265668 Reinhard Zumkeller, <a href="/A265668/b265668.txt">Rows n = 1..1000 of triangle, flattened</a>
%e A265668 .   n | T(n,*)  A5117(n)    n | T(n,*)  A5117(n)    n | T(n,*)   A5117(n)
%e A265668 . ----+---------+------   ----+---------+------   ----+----------+------
%e A265668 .   1 | [1]     |  1       21 | [3,11]  | 33       41 | [2,3,11] | 66
%e A265668 .   2 | [2]     |  2       22 | [2,17]  | 34       42 | [67]     | 67
%e A265668 .   3 | [3]     |  3       23 | [5,7]   | 35       43 | [3,23]   | 69
%e A265668 .   4 | [5]     |  5       24 | [37]    | 37       44 | [2,5,7]  | 70
%e A265668 .   5 | [2,3]   |  6       25 | [2,19]  | 38       45 | [71]     | 71
%e A265668 .   6 | [7]     |  7       26 | [3,13]  | 39       46 | [73]     | 73
%e A265668 .   7 | [2,5]   | 10       27 | [41]    | 41       47 | [2,37]   | 74
%e A265668 .   8 | [11]    | 11       28 | [2,3,7] | 42       48 | [7,11]   | 77
%e A265668 .   9 | [13]    | 13       29 | [43]    | 43       49 | [2,3,13] | 78
%e A265668 .  10 | [2,7]   | 14       30 | [2,23]  | 46       50 | [79]     | 79
%e A265668 .  11 | [3,5]   | 15       31 | [47]    | 47       51 | [2,41]   | 82
%e A265668 .  12 | [17]    | 17       32 | [3,17]  | 51       52 | [83]     | 83
%e A265668 .  13 | [19]    | 19       33 | [53]    | 53       53 | [5,17]   | 85
%e A265668 .  14 | [3,7]   | 21       34 | [5,11]  | 55       54 | [2,43]   | 86
%e A265668 .  15 | [2,11]  | 22       35 | [3,19]  | 57       55 | [3,29]   | 87
%e A265668 .  16 | [23]    | 23       36 | [2,29]  | 58       56 | [89]     | 89
%e A265668 .  17 | [2,13]  | 26       37 | [59]    | 59       57 | [7,13]   | 91
%e A265668 .  18 | [29]    | 29       38 | [61]    | 61       58 | [3,31]   | 93
%e A265668 .  19 | [2,3,5] | 30       39 | [2,31]  | 62       59 | [2,47]   | 94
%e A265668 .  20 | [31]    | 31       40 | [5,13]  | 65       60 | [5,19]   | 95  .
%t A265668 FactorInteger[#][[All,1]]&/@Select[Range[100],SquareFreeQ]//Flatten (* _Harvey P. Dale_, Apr 27 2018 *)
%o A265668 (Haskell)
%o A265668 import Math.NumberTheory.Primes.Factorisation (factorise)
%o A265668 import Data.Maybe (mapMaybe)
%o A265668 a265668 n k = a265668_tabf !! (n-1) !! (k-1)
%o A265668 a265668_row n = a265668_tabf !! (n-1)
%o A265668 a265668_tabf = [1] : mapMaybe f [2..] where
%o A265668    f x = if all (== 1) es then Just ps else Nothing
%o A265668          where (ps, es) = unzip $ factorise x
%Y A265668 Cf. A005117, A027748, A124010, A072047 (row lengths), A073481, A073482, A001221, A111060, A049200, A062822.
%K A265668 nonn,tabf
%O A265668 1,2
%A A265668 _Reinhard Zumkeller_, Dec 13 2015