

A156688


The total number of distinct Pythagorean triples with an area numerically equal to n times their perimeters


2



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, 12, 18, 27, 6, 18, 18, 9, 6, 36, 18, 9, 18, 15, 6, 45, 18, 12, 18, 9, 18
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OFFSET

1,1


COMMENTS

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.
Also, the total number of distinct "areas with equal border", that is: Let x, y be positive integers so that the area xy equals the border around it with thickness n. As a formula it is: 2xy = (x+2n)(y+2n). To compare with the original, the areas at thickness 5 are 11x210, 12x110, 14x60, 15x50, 18x35, 20x30.  Juhani Heino, Jul 22 2012


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



FORMULA



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]


PROG



CROSSREFS



KEYWORD

easy,nice,nonn


AUTHOR



EXTENSIONS



STATUS

approved



