%I #21 Sep 08 2022 08:45:05

%S 30,240,840,5544,6864,26520,23256,73416,208104,107880,467976,473304,

%T 296184,727560,1494600,2101344,863760,3138816,2625864,1492704,5259504,

%U 4248936,7623384,12845904,7759224,4244424

%N Areas of Pythagorean triangles (A069482, A069484, A069486).

%H Marius A. Burtea, <a href="/A069487/b069487.txt">Table of n, a(n) for n = 1..5000</a>

%H César Aguilera, <a href="https://hal.archives-ouvertes.fr/hal-02909691">Two Prime Number Objects and The Velucchi Numbers</a>, hal-02909691 [math.NT], 2020.

%F a(n) = A030078(n+1)*A000040(n) - A000040(n+1)*A030078(n).

%F a(n) = A000040(n+1)^3*A000040(n) - A000040(n+1)*A000040(n)^3.

%F a(n) = A000040(n)*A127917(n+1) - A127917(n)*A000040(n+1). - _César Aguilera_, Sep 18 2019

%e prime(2)^3 * prime(1) - prime(1)^3 * prime(2) = 3^3 * 2 - 2^3 * 3 = 54 - 24 = 30 that is the area of the Pythagorean triangle (5, 12, 13), so a(1) = 30. - _Bernard Schott_, Sep 23 2019

%o (Magma) [NthPrime(n+1)^3*NthPrime(n)-NthPrime(n+1)*(NthPrime(n)^3):n in [1..26]]; // _Marius A. Burtea_, Sep 19 2019

%Y Cf. A069482, A069484, A069486.

%Y Cf. A000040, A030078, A127917.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Mar 29 2002