A127731 Triangle read by rows, where row n consists of the r's where r = (n*m)/(n+m) and the m's are positive integers such that (n+m) divides (n*m).

1, 2, 2, 3, 4, 2, 3, 4, 5, 6, 4, 6, 7, 6, 8, 5, 6, 8, 9, 10, 3, 4, 6, 8, 9, 10, 11, 12, 7, 10, 12, 13, 6, 10, 12, 14, 8, 12, 14, 15, 16, 6, 9, 12, 14, 15, 16, 17, 18, 4, 10, 12, 15, 16, 18, 19, 12, 14, 18, 20, 11, 18, 20, 21, 22, 6, 8, 12, 15, 16, 18, 20, 21, 22, 23, 20, 24, 13, 22, 24, 25

Offset

2,2

Comments

The maximum term of the n-th row, for n >= 2, is (n-1). The minimum term of row n is A063428(n), for n >= 3. 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-j)*(p^j -1), 1<=j<=k.)

Links

Table of n, a(n) for n=2..82.

Example

Row 6 is (2,3,4,5) because row 6 of irregular array A127730 is (3,6,12,30); and (6*3)/(6+3) = 2, (6*6)/(6+6) = 3, (6*12)/(6+12) = 4 and (6*30)/(6+30) = 5.

Mathematica

f[n_] := Select[Table[n*m/(n + m), {m, n^2}], IntegerQ]; Table[f[n], {n, 2, 26}] // Flatten (* Ray Chandler, Feb 13 2007 *)

Crossrefs

Cf. A063428, A063647, A127730.

Sequence in context: A352340 A117632 A236241 * A159978 A230546 A286617

Adjacent sequences: A127728 A127729 A127730 * A127732 A127733 A127734

Keyword

nonn,tabf

Author

Leroy Quet, Jan 26 2007

Extensions

Extended by Ray Chandler, Feb 13 2007

Status

approved