|
| |
|
|
A009112
|
|
Areas of Pythagorean triangles: numbers which can be the area of a right-angled triangle with integer sides.
|
|
17
| |
|
|
6, 24, 30, 54, 60, 84, 96, 120, 150, 180, 210, 216, 240, 270, 294, 330, 336, 384, 480, 486, 504, 540, 546, 600, 630, 720, 726, 750, 756, 840, 864, 924, 960, 990, 1014, 1080, 1176, 1224, 1320, 1344, 1350, 1386, 1470, 1500, 1536, 1560, 1620, 1710, 1716, 1734, 1890
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| Number of terms < 10^k for increasing values of k: 1, 7, 34, 150, 636, 2536, 9757, 35987, 125350, 407538, ..., .
All terms are divisible by 6.
|
|
|
REFERENCES
| S. Mohanty and S. P. Mohanty, Pythagorean Numbers, Fibonacci Quarterly 28 (1990), 31-42
B. Miller, Nasty Numbers, The Mathematics Teacher 73 (1980) page 649
|
|
|
LINKS
| R. Knott, Pythagorean Triangles
|
|
|
EXAMPLE
| 30 belongs to the sequence as the area of the triangle (5,12,13) is 30.
6 is in the sequence because it is the area of the 3-4-5 triangle is the integer 6.
|
|
|
MATHEMATICA
| lst = {}; Do[ If[ IntegerQ[c = Sqrt[a^2 + b^2]], AppendTo[lst, a*b/2]; lst = Union@ lst], {a, 4, 180}, {b, a - 1, Floor[ Sqrt[a]], -1}]; Take[lst, 51] (*From Vladimir Joseph Stephan Orlovsky (4vladimir(AT)gmail.com), 23 Nov 2010*)
|
|
|
PROG
| (PARI) is_A009112(n)={ my(N=1+#n=divisors(2*n)); for( i=1, N\2, issquare(n[i]^2+n[N-i]^2) & return(1)) } \\ - M. F. Hasler, Dec 09 2010
(Sage) is_A009112 = lambda n: any(is_square(a**2+(2*n/a)**2) for a in divisors(2*n)) # [D. S. McNeil, Dec 09 2010]
|
|
|
CROSSREFS
| Union of A009111, A009127, A024365, A177021.
Sequence in context: A131906 A046131 A009111 * A057101 A057228 A132398
Adjacent sequences: A009109 A009110 A009111 * A009113 A009114 A009115
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
|
| |
|
|
