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A060800 a(n) = p^2 + p + 1 where p runs through the primes.

%I A060800 #56 Nov 07 2022 07:39:34
%S A060800 7,13,31,57,133,183,307,381,553,871,993,1407,1723,1893,2257,2863,3541,
%T A060800 3783,4557,5113,5403,6321,6973,8011,9507,10303,10713,11557,11991,
%U A060800 12883,16257,17293,18907,19461,22351,22953,24807,26733,28057,30103,32221
%N A060800 a(n) = p^2 + p + 1 where p runs through the primes.
%C A060800 Terms are divisible by 3 iff p is of the form 6*m+1 (A002476). - _Michel Marcus_, Jan 15 2017
%H A060800 Harry J. Smith, <a href="/A060800/b060800.txt">Table of n, a(n) for n = 1..1000</a>
%H A060800 R. J. Mathar, <a href="/A060800/a060800.pdf">No common terms in the sequences sigma(p^i) and sigma(p^(i+1)) as p runs through the primes</a>.
%F A060800 a(n) = A036690(n) + 1.
%F A060800 a(n) = 1 + A008864(n)*A000040(n) = (A030078(n) - 1)/A006093(n). - _Reinhard Zumkeller_, Aug 06 2007
%F A060800 a(n) = sigma(prime(n)^2) = A000203(A000040(n)^2). - _Zak Seidov_, Feb 13 2016
%F A060800 a(n) = A000203(A001248(n)). - _Michel Marcus_, Feb 15 2016
%F A060800 Product_{n>=1} (1 - 1/a(n)) = zeta(3)/zeta(2) (A253905). - _Amiram Eldar_, Nov 07 2022
%e A060800 a(3) = 31 because 5^2 + 5 + 1 = 31.
%p A060800 A060800:= n -> map (p -> p^(2)+p+1, ithprime(n)):
%p A060800 seq (A060800(n), n=1..41); # _Jani Melik_, Jan 25 2011
%t A060800 #^2 + # + 1&/@Prime[Range[200]] (* _Vincenzo Librandi_, Mar 20 2014 *)
%o A060800 (PARI) { n=0; forprime (p=2, prime(1000), write("b060800.txt", n++, " ", p^2 + p + 1); ) } \\ _Harry J. Smith_, Jul 13 2009
%o A060800 (Magma) [p^2+p+1: p in PrimesUpTo(200)]; // _Vincenzo Librandi_, Mar 20 2014
%Y A060800 Cf. A001248, A131991, A131992, A131993, A253905.
%Y A060800 Cf. A008864, A000203. - _Zak Seidov_, Feb 13 2016
%K A060800 nonn,easy
%O A060800 1,1
%A A060800 _Jason Earls_, Apr 27 2001
%E A060800 More terms from Larry Reeves (larryr(AT)acm.org), May 03 2001