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 A056538 Irregular triangle read by rows: row n lists divisors of n in decreasing order. 18
 1, 2, 1, 3, 1, 4, 2, 1, 5, 1, 6, 3, 2, 1, 7, 1, 8, 4, 2, 1, 9, 3, 1, 10, 5, 2, 1, 11, 1, 12, 6, 4, 3, 2, 1, 13, 1, 14, 7, 2, 1, 15, 5, 3, 1, 16, 8, 4, 2, 1, 17, 1, 18, 9, 6, 3, 2, 1, 19, 1, 20, 10, 5, 4, 2, 1, 21, 7, 3, 1, 22, 11, 2, 1, 23, 1, 24, 12, 8, 6, 4, 3, 2, 1, 25, 5, 1, 26, 13, 2, 1, 27, 9 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Old name was "Replace n by its divisors in reverse order." This gives the second elements of the ordered pairs (a,b), a >= 1, b >= 1, ordered by their product ab. T(n,k) = n / A027750(n,k) = A027750(n,n-k+1), 1 <= k <= A000005(n). - Reinhard Zumkeller, Sep 28 2014 LINKS Reinhard Zumkeller, Rows n = 1..1000 of triangle, flattened Omar E. Pol, Illustration of the divisors of n - Omar E. Pol, Nov 22 2009 FORMULA a(n) = A064894(A064896(n)). EXAMPLE Triangle begins: 1; 2, 1; 3, 1; 4, 2, 1; 5, 1; 6, 3, 2, 1; 7, 1; 8, 4, 2, 1; 9, 3, 1; 10, 5, 2, 1; 11, 1; 12, 6, 4, 3, 2, 1; 13, 1; 14, 7, 2, 1; 15, 5, 3, 1; 16, 8, 4, 2, 1; 17, 1; 18, 9, 6, 3, 2, 1; 19, 1; 20, 10, 5, 4, 2, 1; MAPLE map(op, [seq(reverse(sort(divisors(j))), j=1..30)]); cdr := proc(l) if 0 = nops(l) then ([]) else (l[2..nops(l)]): fi: end: reverse := proc(l) if 0 = nops(l) then ([]) else [op(reverse(cdr(l))), l[1]]; fi: end: MATHEMATICA Table[Reverse@ Divisors@ n, {n, 27}] // Flatten (* Michael De Vlieger, Jul 27 2016 *) PROG (MAGMA) [Reverse(Divisors(n)) : n in [1..30]]; (Haskell) a056538 n k = a056538_tabf !! (n-1) !! (k-1) a056538_row n = a056538_tabf !! (n-1) a056538_tabf = map reverse a027750_tabf -- Reinhard Zumkeller, Sep 28 2014 (PARI) row(n)=Vecrev(divisors(n)) \\ Charles R Greathouse IV, Sep 02 2015 CROSSREFS Cf. A027750 for the first elements, A056534, A168017, A000005 (row lengths), A000203 (row sums). Sequence in context: A210959 A319848 A233772 * A266742 A120385 A216477 Adjacent sequences:  A056535 A056536 A056537 * A056539 A056540 A056541 KEYWORD nonn,tabf AUTHOR Antti Karttunen, Jun 20, 2000 EXTENSIONS Definition revised by N. J. A. Sloane, Jul 27 2016 STATUS approved

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Last modified January 21 02:59 EST 2019. Contains 319344 sequences. (Running on oeis4.)