OFFSET
1,1
COMMENTS
Distribution of edge-length occurrences for Euler bricks is remarkably near-uniform.
REFERENCES
L. E. Dickson, History of the Theory of Numbers, vol. 2, Diophantine Analysis, Dover, New York, 2005.
P. Halcke, Deliciae Mathematicae; oder, Mathematisches sinnen-confect., N. Sauer, Hamburg, Germany, 1719, page 265.
LINKS
Robin Visser, Table of n, a(n) for n = 1..10000
E. W. Weisstein, MathWorld: Euler brick
EXAMPLE
For n=1 (i.e., the integers 1..100), there are only 3 possible edge-lengths for Euler bricks: 44, 85, 88.
PROG
(Sage)
def a(n):
ans = set()
for x in range(100*(n-1)+1, 100*n+1):
divs = Integer(x^2).divisors()
for d in divs:
if (d <= x^2/d): continue
if (d-x^2/d)%2==0:
y = (d-x^2/d)/2
for e in divs:
if (e <= x^2/e): continue
if (e-x^2/e)%2==0:
z = (e-x^2/e)/2
if (y^2+z^2).is_square(): ans.add(x)
return len(ans) # Robin Visser, Jan 02 2024
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Christopher Monckton of Brenchley, Oct 08 2011
STATUS
approved