OFFSET
1,1
COMMENTS
This sequence also gives Fibonacci's congruous numbers (or congrua) divided by 4 with multiplicities, not regarding leg exchange in the underlying primitive Pythagorean triangle. See A258150 and the example. - Wolfdieter Lang, Jun 14 2015
The squarefree part of an entry which is not squarefree is a primitive congruent number from A006991 belonging to a Pythagorean triangle with rational (not all integer) side lengths (and its companion obtained by exchanging the legs). See the W. Lang link. - Wolfdieter Lang, Oct 25 2016
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..10000
Ron Knott, Pythagorean Triples and Online Calculators
Eric Weisstein's World of Mathematics, Congruum Problem
FORMULA
a(n) = 6*A020885(n). - Lekraj Beedassy, Apr 30 2004
EXAMPLE
a(6) = a(7) = 210 corresponds to the area (in some squared length unit) of the primitive Pythagorean triangles (21, 20, 29) and (35, 12, 37). Fibonacci's congruum C = 840 = 210*4 belongs to the two triples [x, y, z] = [29, 41, 1] and [37, 47, 23], solving x^2 + C = y^2 and x^2 - C = z^2. - Wolfdieter Lang, Jun 14 2015
a(5) = 180 = 6^2*5 lead to the primitive congruent number A006991(1) = 5 from the primitive Pythagorean triangle [9, 40, 41] after division by 6: [3/2, 20/3, 41/6]. See the link for the other nonsquarefree a(n) numbers. - Wolfdieter Lang, Oct 25 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved