OFFSET
1,1
COMMENTS
FORMULA
a(n,m) = numerator(2/n + 1/m), n >= m >= 1, and 0 otherwise.
A221918(n,m)/a(n,m) = R(n,m) = n*m/(n+m). 1/R(n,m) = 1/n + 1/m.
EXAMPLE
The triangle a(n,m) begins:
n\m 1 2 3 4 5 6 7 8 9 10 11 12 ...
1: 2
2: 3 1
3: 4 5 2
4: 5 3 7 1
5: 6 7 8 9 2
6: 7 2 1 5 11 1
7: 8 9 10 11 12 13 2
8: 9 5 11 3 13 7 15 1
9: 10 11 4 13 14 5 16 17
10: 11 3 13 7 3 4 17 9 19 1
11: 12 13 14 15 16 17 18 15 20 21 2
12: 13 7 5 1 17 1 19 5 7 11 23 1
...
a(n,1) = n + 1 because R(n,1) = n/(n+1), gcd(n,n+1) = 1, hence denominator(R(n,m)) = n + 1.
a(5,4) = 9 because R(5,4) = 20/9, gcd(20,9) = 1, hence denominator( R(5,4)) = 9.
a(6,3) = 1 because R(6,3) = 18/9 = 2/1.
For the rationals R(n,m) see A221918.
MATHEMATICA
a[n_, m_] := Numerator[1/n + 1/m]; Table[a[n, m], {n, 1, 12}, {m, 1, n}] // Flatten (* Jean-François Alcover, Feb 25 2013 *)
CROSSREFS
KEYWORD
AUTHOR
Wolfdieter Lang, Feb 21 2013
STATUS
approved