A079704 a(n) = 2*prime(n)^2.

8, 18, 50, 98, 242, 338, 578, 722, 1058, 1682, 1922, 2738, 3362, 3698, 4418, 5618, 6962, 7442, 8978, 10082, 10658, 12482, 13778, 15842, 18818, 20402, 21218, 22898, 23762, 25538, 32258, 34322, 37538, 38642, 44402, 45602, 49298, 53138, 55778

Offset: 1

Author

Jon Perry, Jan 31 2003

Keywords

• easy
• nonn

Comments

Numbers of the form 2*p^2 where p runs through the primes.

For these numbers m, there are precisely 5 groups of order m, hence this is a subsequence of A054397. If p = 2, these 5 groups of order 8 are described in example section of A054397, and when p is odd prime, the five corresponding groups are described in a comment of A143928. - Bernard Schott, Dec 11 2021

Examples

			a(2) = prime(2)^2*2 = 3^2*2 = 9*2 = 18.
		

References

• Pascal Ortiz, Exercices d'Algèbre, Collection CAPES / Agrégation, Ellipses, problème 1.35, pp. 70-74, 2004.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A001248, A054397, A100484.

A143928 is a subsequence.

Programs

Haskell

a079704 = (* 2) . a001248  -- Reinhard Zumkeller, Nov 19 2013

Magma

[2*p^2: p in PrimesUpTo(200)]; // Vincenzo Librandi, Mar 27 2014

Mathematica

2 Prime[Range[40]]^2 (* Vincenzo Librandi, Mar 27 2014 *)

PARI

forprime (p=2,100,print1(p^2*2","))

Python

from sympy import primerange
print([2*p**2 for p in primerange(1, 200)]) # Michael S. Branicky, Dec 11 2021

Formula

a(n) = 2*A001248(n) = A100484(n)*A000040(n). - Reinhard Zumkeller, Nov 19 2013

Extensions

More terms from Vincenzo Librandi, Jan 29 2010

Offset corrected by Reinhard Zumkeller, Nov 19 2013