

A127730


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


16



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
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OFFSET

2,1


COMMENTS

The maximum term of the nth row, for n >= 2, is n*(n1). 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*(nd_n(k))/d_n(k).  Franklin T. AdamsWatters, 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*(n1) 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 *)


PROG

(PARI) arow(n)=local(d, m); d=divisors(n^2); vector(#d\2, k, m=d[ #d\2k+1]; n*(nm)/m) \\ Franklin T. AdamsWatters, 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



