A069487 Areas of Pythagorean triangles (A069482, A069484, A069486).

30, 240, 840, 5544, 6864, 26520, 23256, 73416, 208104, 107880, 467976, 473304, 296184, 727560, 1494600, 2101344, 863760, 3138816, 2625864, 1492704, 5259504, 4248936, 7623384, 12845904, 7759224, 4244424

Offset: 1

Author

Reinhard Zumkeller, Mar 29 2002

Keywords

• nonn

Examples

			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
		

Links

• Marius A. Burtea, Table of n, a(n) for n = 1..5000
• César Aguilera, Two Prime Number Objects and The Velucchi Numbers, hal-02909691 [math.NT], 2020.

Crossrefs

Cf. A069482, A069484, A069486.

Cf. A000040, A030078, A127917.

Programs

Magma

[NthPrime(n+1)^3*NthPrime(n)-NthPrime(n+1)*(NthPrime(n)^3):n in [1..26]]; // Marius A. Burtea, Sep 19 2019

Formula

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

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

a(n) = A000040(n)*A127917(n+1) - A127917(n)*A000040(n+1). - César Aguilera, Sep 18 2019