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 A027751 Irregular triangle read by rows in which row n lists the proper divisors of n (those divisors of n which are < n), with the first row {1} by convention. 42
 1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 4, 1, 3, 1, 2, 5, 1, 1, 2, 3, 4, 6, 1, 1, 2, 7, 1, 3, 5, 1, 2, 4, 8, 1, 1, 2, 3, 6, 9, 1, 1, 2, 4, 5, 10, 1, 3, 7, 1, 2, 11, 1, 1, 2, 3, 4, 6, 8, 12, 1, 5, 1, 2, 13, 1, 3, 9, 1, 2, 4, 7, 14, 1, 1, 2, 3, 5, 6, 10, 15, 1, 1, 2, 4, 8, 16, 1, 3, 11, 1, 2, 17, 1, 5, 7, 1, 2, 3, 4, 6, 9, 12, 18 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Or, take the list 1,2,3,4,... of natural numbers (A000027) and replace each number by its proper divisors. The row length is 1 for n = 1 and A032741(n) for n >= 2. - Wolfdieter Lang, Jan 16 2016 LINKS Alois P. Heinz, Rows n = 1..1540, flattened EXAMPLE The irregular triangle T(n,k) begins: n\k  1 2 3 4  5 ... 1:   1  (by convention) 2:   1 3:   1 4:   1 2 5:   1 6:   1 2 3 7:   1 8:   1 2 4 9:   1 3 10:  1 2 5 11:  1 12:  1 2 3 4  6 13:  1 14:  1 2 7 15:  1 3 5 16:  1 2 4 8 17:  1 18:  1 2 3 6  9 19:  1 20:  1 2 4 5 10 .... reformatted - Wolfdieter Lang, Jan 16 2016 MAPLE with(numtheory): T:= n-> sort([(divisors(n) minus {n})[]])[]: T(1):=1: seq(T(n), n=1..50); # Alois P. Heinz, Apr 11 2012 MATHEMATICA Table[ Divisors[n] // Most, {n, 1, 36}] // Flatten // Prepend[#, 1] & (* Jean-François Alcover, Jun 10 2013 *) PROG (Haskell) a027751 n k = a027751_tabf !! (n-1) !! (k-1) a027751_row n = a027751_tabf !! (n-1) a027751_tabf = [1] : map init (tail a027750_tabf) -- Reinhard Zumkeller, Apr 18 2012 (Python) from sympy import divisors def a(n): return [1] if n==1 else divisors(n)[:-1] for n in range(21): print(a(n)) # Indranil Ghosh, Apr 30 2017 (PARI) row(n) = if (n==1, [1], my(d = divisors(n)); vector(#d-1, k, d[k])); \\ Michel Marcus, Apr 30 2017 CROSSREFS Cf. A027750, A032741 (row lengths), A001065, A000005. Row sums give A173455. - Omar E. Pol, Nov 23 2010 Sequence in context: A228107 A140207 A104763 * A181322 A004070 A180562 Adjacent sequences:  A027748 A027749 A027750 * A027752 A027753 A027754 KEYWORD nonn,easy,tabf AUTHOR EXTENSIONS More terms from Patrick De Geest, May 15 1998 Example edited by Omar E. Pol, Nov 23 2010 STATUS approved

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Last modified November 27 23:46 EST 2020. Contains 338684 sequences. (Running on oeis4.)