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A265110
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Partial row products of table A027746, prime factors with repetition.
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3
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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, 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, 6, 30, 31, 2, 4, 8, 16, 32, 3, 33, 2, 34, 5, 35, 2, 4, 12, 36
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OFFSET
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1,2
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COMMENTS
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T(n,1) = A020639(n); T(n,A001222(n)) = n.
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LINKS
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Reinhard Zumkeller, Rows n = 1..1000 of triangle, flattened
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FORMULA
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T(n,k) = product(A027747(n,k): k = 1 .. A001221(n)).
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EXAMPLE
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. n | T(n,*) | A027746(n,*)
. ----+----------------+----------------
. 1 | 1 | 1
. 2 | 2 | 2
. 3 | 3 | 3
. 4 | 2, 4 | 2, 2
. 5 | 5 | 5
. 6 | 2, 6 | 2, 3
. 7 | 7 | 7
. 8 | 2, 4, 8 | 2, 2, 2
. 9 | 3, 9 | 3, 3
. 10 | 2, 10 | 2, 5
. 11 | 11 | 11
. 12 | 2, 4, 12 | 2, 2, 3
. 13 | 13 | 13
. 14 | 2, 14 | 2, 7
. 15 | 3, 15 | 3, 5
. 16 | 2, 4, 8, 16 | 2, 2, 2, 2
. 17 | 17 | 17
. 18 | 2, 6, 18 | 2, 3, 3
. 19 | 19 | 19
. 20 | 2, 4, 20 | 2, 2, 5
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MATHEMATICA
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Table[FoldList[Times, Flatten[FactorInteger[n] /. {p_, e_} /; e > 0 :> ConstantArray[p, e]]], {n, 37}] // Flatten (* Michael De Vlieger, Apr 28 2017 *)
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PROG
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(Haskell)
a265110 n k = a265110_tabf !! (n-1) !! (k-1)
a265110_row n = a265110_tabf !! (n-1)
a265110_tabf = map (scanl1 (*)) a027746_tabf
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CROSSREFS
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Cf. A027746, A175943, A001222 (row lengths), A020639.
Sequence in context: A214595 A357255 A136181 * A304742 A003976 A252371
Adjacent sequences: A265107 A265108 A265109 * A265111 A265112 A265113
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KEYWORD
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nonn,tabf
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AUTHOR
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Reinhard Zumkeller, Dec 01 2015
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STATUS
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approved
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