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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. 58
 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 N. J. A. Sloane. 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 30 19:18 EST 2023. Contains 367462 sequences. (Running on oeis4.)