OFFSET
1,1
COMMENTS
These are numbers which can be written either as b^2*c^2*(b^2+c^2)*d^2 or if (b^2+c^2) is a square then as b^2*c^2*d^2, since 1/(b*(b^2+c^2)*d)^2+1/(c*(b^2+c^2)*d)^2 =1/(b^2*c^2*(b^2+c^2)*d^2) and 1/(b*sqrt(b^2+c^2)*d)^2+1/(c*sqrt(b^2+c^2)*d)^2 = 1/(b^2*c^2*d^2).
EXAMPLE
98 is in the sequence since 1/98=1/10^2+1/70^2 (also 1/98=1/14^2+1/14^2).
PROG
(Python)
from fractions import Fraction
def aupto(lim):
sqr_recips = [Fraction(1, i*i) for i in range(1, lim+2)]
ssr = set(f + g for i, f in enumerate(sqr_recips) for g in sqr_recips[i:])
representable = [f.denominator for f in ssr if f.numerator == 1]
return sorted(r for r in representable if r <= lim)
print(aupto(1800)) # Michael S. Branicky, Feb 08 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Henry Bottomley, Jul 28 2001
EXTENSIONS
Offset changed to 1 by Derek Orr, Jun 23 2015
STATUS
approved