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A027746
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Triangle in which first row is 1, n-th row (n>1) gives prime factors of n with repetition.
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27
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1, 2, 3, 2, 2, 5, 2, 3, 7, 2, 2, 2, 3, 3, 2, 5, 11, 2, 2, 3, 13, 2, 7, 3, 5, 2, 2, 2, 2, 17, 2, 3, 3, 19, 2, 2, 5, 3, 7, 2, 11, 23, 2, 2, 2, 3, 5, 5, 2, 13, 3, 3, 3, 2, 2, 7, 29, 2, 3, 5, 31, 2, 2, 2, 2, 2, 3, 11, 2, 17, 5, 7, 2, 2, 3, 3, 37, 2, 19, 3, 13, 2, 2, 2, 5, 41, 2, 3, 7, 43, 2, 2, 11, 3, 3, 5
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| n-th row has length A001222(n) (n>1).
A001414(n)=Sum(T(n,k):1<=k<=A001222(n)), n>1; A006530(n) = T(n,A001222(n)) = Max(T(n,k):1<=k<=A001222(n)); A020639(n) = T(n,1) = Min(T(n,k):1<=k<=A001222(n)). [Reinhard Zumkeller, Aug 27 2011]
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LINKS
| N. J. A. Sloane, First 2048 rows of triangle, flattened
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FORMULA
| Product(T(n,k): 1 <= k <= A001221(n)) = n.
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EXAMPLE
| 1; 2; 3; 2,2; 5; 2,3; 7; 2,2,2; 3,3; 2,5; ...
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MAPLE
| P:=proc(n) local FM: FM:=ifactors(n)[2]: seq(seq(FM[j][1], k=1..FM[j][2]), j=1..nops(FM)) end: 1; for n from 2 to 45 do P(n) od; # yields sequence in triangular form (Emeric Deutsch, Feb 13 2005)
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MATHEMATICA
| row[n_] := Flatten[ Table[#[[1]], {#[[2]]}] & /@ FactorInteger[n]]; Flatten[ Table[ row[n], {n, 1, 45}]] (* From Jean-François Alcover, Dec 01 2011 *)
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PROG
| (Haskell)
import Data.List (unfoldr)
a027746 n k = a027746_tabl !! (n-1) !! (k-1)
a027746_tabl = map a027746_row [1..]
a027746_row 1 = [1]
a027746_row n = unfoldr fact n where
fact 1 = Nothing
fact x = Just (p, x `div` p) where p = a020639 x
-- Reinhard Zumkeller, Aug 27 2011
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CROSSREFS
| Cf. A000027, A001222, A027748.
a(A022559(A000040(n))+1) = A000040(n).
Cf. A020639.
Sequence in context: A053269 A163873 A118665 * A166454 A128651 A093797
Adjacent sequences: A027743 A027744 A027745 * A027747 A027748 A027749
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KEYWORD
| nonn,easy,nice,tabf
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AUTHOR
| MAGHRAOUI Abdelkader (maghraoui.faure.recherche.entpe(AT)obelix.entpe.fr) [Apparently this email address is defunct]
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu)
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