A079704 - OEIS

%I #35 Sep 08 2022 08:45:08

%S 8,18,50,98,242,338,578,722,1058,1682,1922,2738,3362,3698,4418,5618,

%T 6962,7442,8978,10082,10658,12482,13778,15842,18818,20402,21218,22898,

%U 23762,25538,32258,34322,37538,38642,44402,45602,49298,53138,55778

%N a(n) = 2*prime(n)^2.

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

%C 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

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

%H Reinhard Zumkeller, <a href="/A079704/b079704.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = 2*A001248(n) = A100484(n)*A000040(n). - _Reinhard Zumkeller_, Nov 19 2013

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

%t 2 Prime[Range[40]]^2 (* _Vincenzo Librandi_, Mar 27 2014 *)

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

%o (Haskell)

%o a079704 = (* 2) . a001248  -- _Reinhard Zumkeller_, Nov 19 2013

%o (Magma) [2*p^2: p in PrimesUpTo(200)]; // _Vincenzo Librandi_, Mar 27 2014

%o (Python)

%o from sympy import primerange

%o print([2*p**2 for p in primerange(1, 200)]) # _Michael S. Branicky_, Dec 11 2021

%Y Cf. A000040, A001248, A054397, A100484.

%Y A143928 is a subsequence.

%K easy,nonn

%O 1,1

%A _Jon Perry_, Jan 31 2003

%E More terms from _Vincenzo Librandi_, Jan 29 2010

%E Offset corrected by _Reinhard Zumkeller_, Nov 19 2013