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 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

%I

%S 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,

%T 13,6,10,12,14,8,12,14,15,16,6,9,12,14,15,16,17,18,4,10,12,15,16,18,

%U 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

%N 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).

%C 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.)

%e 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.

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

%Y Cf. A063428, A063647, A127730.

%K nonn,tabf

%O 2,2

%A _Leroy Quet_, Jan 26 2007

%E Extended by _Ray Chandler_, Feb 13 2007

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Last modified May 26 00:32 EDT 2020. Contains 334613 sequences. (Running on oeis4.)