A098996 a(n) = p*(p + 1)*(2*p + 1) where p is the n-th prime.

30, 84, 330, 840, 3036, 4914, 10710, 14820, 25944, 51330, 62496, 105450, 142926, 164604, 214320, 306234, 421260, 465186, 615060, 731016, 794094, 1004880, 1164324, 1433790, 1853670, 2091306, 2217384, 2484540, 2625810, 2924214, 4145280, 4547796, 5199150, 5429340

Offset: 1

Author

Parthasarathy Nambi, Nov 05 2004

Keywords

• nonn

Comments

The unique primitive Pythagorean triple whose inradius is the n-th prime p and whose short leg is an odd number is (2*p+1, 2*p*(p+1), 2*p*(p+1)+1) and its area is a(n) = p*(p+1)*(2*p+1). - Miguel-Ángel Pérez García-Ortega, Mar 16 2025

Examples

			a(4) = 7*(7+1)*(2*7+1) = 840.
		

References

• Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2025.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A034953, A367573, A382097, A382070.

Programs

Magma

[(p*(p+1)*(2*p+1)): p in PrimesUpTo(200)]; // Vincenzo Librandi, Feb 04 2011

Mathematica

#(#+1)(2#+1)&/@Prime[Range[30]] (* Harvey P. Dale, Jun 23 2020 *)

Formula

a(n) = prime(n)*(prime(n)+1)*(2*prime(n)+1).

Extensions

More terms from Klaus Brockhaus, Nov 09 2004