OFFSET
1,1
COMMENTS
(a, b, c) is an ABC triple if gcd(a, b) = 1 and a + b = c. ABC triples with c > rad(a*b*c) are called "abc-hits". For primitive Pythagorean triples (u, v, w) it is u^2 + v^2 = w^2 and gcd(u^2, v^2) = 1. (u^2, v^2, w^2) are therefore ABC triples. They are then "abc-hits" if in addition w^2 > rad(u^2*v^2*w^2). If (u, v, w) is a non-primitive Pythagorean triple, (u^2, v^2, w^2) is not an ABC triple.
w of primitive Pythagorean triples (u, v, w) with A007947(u^2*v^2*w^2) < w^2.
LINKS
Abderrahmane Nitaj, The ABC Conjecture Home Page
Wikipedia, abc conjecture
EXAMPLE
25 from the primitive Pythagorean triple (7, 24, 25) is in the sequence, because 7^2 + 24^2 = 25^2, gcd(7^2, 24^2) = 1 and 25^2 = 625 > rad(7^2*24^2*25^2) = 7*2*3*5 = 210.
CROSSREFS
KEYWORD
nonn
AUTHOR
Felix Huber, Oct 13 2023
STATUS
approved