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
The 2nd column of the triangle is the largest proper divisor (A032742). - Charles Kusniec, Jan 30 2021
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
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
KEYWORD
nonn,tabf
AUTHOR
Antti Karttunen, Jun 20, 2000
EXTENSIONS
Definition revised by N. J. A. Sloane, Jul 27 2016
STATUS
approved