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%I #12 Apr 29 2017 04:30:57
%S 1,2,3,2,4,5,2,6,7,2,4,8,3,9,2,10,11,2,4,12,13,2,14,3,15,2,4,8,16,17,
%T 2,6,18,19,2,4,20,3,21,2,22,23,2,4,8,24,5,25,2,26,3,9,27,2,4,28,29,2,
%U 6,30,31,2,4,8,16,32,3,33,2,34,5,35,2,4,12,36
%N Partial row products of table A027746, prime factors with repetition.
%C T(n,1) = A020639(n); T(n,A001222(n)) = n.
%H Reinhard Zumkeller, <a href="/A265110/b265110.txt">Rows n = 1..1000 of triangle, flattened</a>
%F T(n,k) = product(A027747(n,k): k = 1 .. A001221(n)).
%e . n | T(n,*) | A027746(n,*)
%e . ----+----------------+----------------
%e . 1 | 1 | 1
%e . 2 | 2 | 2
%e . 3 | 3 | 3
%e . 4 | 2, 4 | 2, 2
%e . 5 | 5 | 5
%e . 6 | 2, 6 | 2, 3
%e . 7 | 7 | 7
%e . 8 | 2, 4, 8 | 2, 2, 2
%e . 9 | 3, 9 | 3, 3
%e . 10 | 2, 10 | 2, 5
%e . 11 | 11 | 11
%e . 12 | 2, 4, 12 | 2, 2, 3
%e . 13 | 13 | 13
%e . 14 | 2, 14 | 2, 7
%e . 15 | 3, 15 | 3, 5
%e . 16 | 2, 4, 8, 16 | 2, 2, 2, 2
%e . 17 | 17 | 17
%e . 18 | 2, 6, 18 | 2, 3, 3
%e . 19 | 19 | 19
%e . 20 | 2, 4, 20 | 2, 2, 5
%t Table[FoldList[Times, Flatten[FactorInteger[n] /. {p_, e_} /; e > 0 :> ConstantArray[p, e]]], {n, 37}] // Flatten (* _Michael De Vlieger_, Apr 28 2017 *)
%o (Haskell)
%o a265110 n k = a265110_tabf !! (n-1) !! (k-1)
%o a265110_row n = a265110_tabf !! (n-1)
%o a265110_tabf = map (scanl1 (*)) a027746_tabf
%Y Cf. A027746, A175943, A001222 (row lengths), A020639.
%K nonn,tabf
%O 1,2
%A _Reinhard Zumkeller_, Dec 01 2015
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