A364109 -id:A364109 - cp's OEIS frontend

A364110 a(n) = sqrt((x^2 - y^2)xy/c) where x is A364108(n), y is A364109(n) and c is A006991(n).

6, 1, 60, 9690, 6, 2, 2, 105, 72306780, 90090, 1, 103320, 6, 4737551070, 118575, 10, 60, 462, 12111037689240, 297855654284978790, 1170, 9147755349330, 121068780, 6, 1976, 3, 281820, 63600, 15, 495683115837000, 462, 4641, 3353350, 49210, 3974124, 49062, 59085715926389725950, 35

Offset: 1

Michel Marcus, Jul 05 2023

nonn

Michel Marcus, Table of n, a(n) for n = 1..361
Mauro Fiorentini, Numeri congruenti minori di 1000. See column r.

Cf. A006991 (primitive congruent numbers), A364108 (x), A364109 (y).

A364108 a(n) is the larger coefficient of the pair (x, y) such that (x^2-y^2)/r, 2xy/r, (x^2+y^2)/r are the 2 legs and hypotenuse of the least Pythagorean triple having area A006991(n).

Original entry on oeis.org

5, 2, 16, 325, 8, 4, 4, 50, 24336, 4901, 3, 1600, 9, 777925, 1250, 13, 25, 72, 14561856, 1873180325, 125, 12079525, 39200, 9, 192, 7, 3600, 2816, 26, 169000000, 85, 338, 17956, 1444, 14112, 1445, 44715091781, 50, 8780605285453456, 2725, 10, 37, 716311250, 144, 306317326339867638016

Offset: 1

Michel Marcus, Jul 05 2023

nonn

Michel Marcus, Table of n, a(n) for n = 1..361
Mauro Fiorentini, Numeri congruenti minori di 1000. See column a.
David Goldberg, Triangle Sides for Congruent Numbers less than 10,000, arXiv:2106.07373 [math.NT], 2021. See column P, p. 7.
Hisanori Mishima, Congruum. See column m.

Cf. A006991 (primitive congruent numbers), A364109 (y), A364110 (r).

cp's OEIS Frontend

A364110 a(n) = sqrt((x^2 - y^2)xy/c) where x is A364108(n), y is A364109(n) and c is A006991(n).

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A364108 a(n) is the larger coefficient of the pair (x, y) such that (x^2-y^2)/r, 2xy/r, (x^2+y^2)/r are the 2 legs and hypotenuse of the least Pythagorean triple having area A006991(n).

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cp's OEIS Frontend

A364110 a(n) = sqrt((x^2 - y^2)*x*y/c) where x is A364108(n), y is A364109(n) and c is A006991(n).

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A364108 a(n) is the larger coefficient of the pair (x, y) such that (x^2-y^2)/r, 2*x*y/r, (x^2+y^2)/r are the 2 legs and hypotenuse of the least Pythagorean triple having area A006991(n).

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A364110 a(n) = sqrt((x^2 - y^2)xy/c) where x is A364108(n), y is A364109(n) and c is A006991(n).

A364108 a(n) is the larger coefficient of the pair (x, y) such that (x^2-y^2)/r, 2xy/r, (x^2+y^2)/r are the 2 legs and hypotenuse of the least Pythagorean triple having area A006991(n).