A127730 Triangle read by rows: row n consists of the positive integers m where m+n divides m*n.

2, 6, 4, 12, 20, 3, 6, 12, 30, 42, 8, 24, 56, 18, 72, 10, 15, 40, 90, 110, 4, 6, 12, 24, 36, 60, 132, 156, 14, 35, 84, 182, 10, 30, 60, 210, 16, 48, 112, 240, 272, 9, 18, 36, 63, 90, 144, 306, 342, 5, 20, 30, 60, 80, 180, 380, 28, 42, 126, 420, 22, 99, 220, 462

Offset

2,1

Comments

The maximum term of the n-th row, for n >= 2, is n*(n-1). The minimum term of row n is A063427(n). Row n contains A063647(n) terms (according to a comment by Benoit Cloitre). For p prime, row p^k has k terms. (Each term in row p^k is of the form p^k*(p^j -1), 1 <= j <= k.)

Links

Nathaniel Johnston, Rows n = 2..500, flattened

Formula

Let d_n be the sequence of divisors of n^2 that are less than n, in reverse order. Then T(n,k) = n*(n-d_n(k))/d_n(k). - Franklin T. Adams-Watters, Aug 07 2009

Example

Row 6 is (3,6,12,30) because 6+3 = 9 divides 6*3 = 18, 6+6 = 12 divides 6*6 = 36, 6+12 = 18 divides 6*12 = 72 and 6+30 = 36 divides 6*30 = 180.

Maple

for n from 2 to 20 do for m from 1 to n*(n-1) do if(m*n mod (m+n) = 0)then printf("%d, ", m): fi: od: od: # Nathaniel Johnston, Jun 22 2011

Mathematica

f[n_] := Select[Range[n^2], Mod[n*#, n + # ] == 0 &]; Table[f[n], {n, 2, 24}] // Flatten (* Ray Chandler, Feb 13 2007 *)

Prog

(PARI) arow(n)=local(d, m); d=divisors(n^2); vector(#d\2, k, m=d[ #d\2-k+1]; n*(n-m)/m) \\ Franklin T. Adams-Watters, Aug 07 2009

Crossrefs

Cf. A063427, A063647, A127731, A191973.

Sequence in context: A007517 A072946 A134000 * A118416 A046204 A163755

Adjacent sequences: A127727 A127728 A127729 * A127731 A127732 A127733

Keyword

nonn,easy,tabf

Author

Leroy Quet, Jan 26 2007

Extensions

Extended by Ray Chandler, Feb 13 2007

Status

approved