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
Antti Karttunen, Table of n, a(n) for n = 1..65537
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
(PARI) A156688(n) = (numdiv(8*n*n)/2); \\ Antti Karttunen, Sep 27 2018
CROSSREFS
KEYWORD
easy,nice,nonn
AUTHOR
Ant King, Feb 18 2009
EXTENSIONS
More terms from Antti Karttunen, Sep 27 2018
STATUS
approved