|
Search: id:A156688
|
|
|
| A156688 |
|
The total number of distinct Pythagorean triples with an area numerically equal to n times their perimeters |
|
+0
1
|
|
| 2, 3, 6, 4, 6, 9, 6, 5, 10, 9, 6, 12, 6, 9, 18, 6, 6, 15, 6, 12, 18, 9, 6, 15, 10, 9, 14, 12, 6, 27, 6, 7, 18, 9, 18, 20, 6, 9, 18, 15, 6, 27, 6, 12, 30, 9, 6, 18, 10, 15, 18, 12, 6, 21, 18, 15, 18, 9, 6, 36, 6, 9, 30, 8, 18, 27, 6, 12, 18, 27, 6, 25, 6, 9, 30
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
The members of this sequence are also 1/2 the number of divisors of 8n^2. The corresponding results for primitive triangles only are in A068068.
|
|
REFERENCES
|
Chi, Henjin and Killgrove, Raymond; Problem 1447, Crux Math 15(5), May 1989.
Chi, Henjin and Killgrove, Raymond; Solution to Problem 1447, Crux Math 16(7), September 1990.
|
|
LINKS
|
Ron Knott, Right-angled Triangles and Pythagoras' Theorem
|
|
FORMULA
|
1/2 d(8n^2)=1/2 A000005(8n^2)
|
|
EXAMPLE
|
There are 6 Pythagorean triples whose area is 5 times their perimeters - (21,220,221), (22,120,122), (24,70,74), (25,60,65),(28,45,53) and (30,40,50) - hence a(5)=6.
|
|
MATHEMATICA
|
1/2 DivisorSigma[0, 8#^2] &/@Range[75]
|
|
CROSSREFS
|
A000005, A068068
Sequence in context: A127915 A072637 A125703 this_sequence A019567 A098286 A138608
Adjacent sequences: A156685 A156686 A156687 this_sequence A156689 A156690 A156691
|
|
KEYWORD
|
easy,nice,nonn
|
|
AUTHOR
|
Ant King (mathstutoring(AT)ntlworld.com), Feb 18 2009
|
|
|
Search completed in 0.002 seconds
|
