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

7, 13, 31, 57, 133, 183, 307, 381, 553, 871, 993, 1407, 1723, 1893, 2257, 2863, 3541, 3783, 4557, 5113, 5403, 6321, 6973, 8011, 9507, 10303, 10713, 11557, 11991, 12883, 16257, 17293, 18907, 19461, 22351, 22953, 24807, 26733, 28057, 30103, 32221

Offset

1,1

Comments

Terms are divisible by 3 iff p is of the form 6*m+1 (A002476). - Michel Marcus, Jan 15 2017

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

R. J. Mathar, No common terms in the sequences sigma(p^i) and sigma(p^(i+1)) as p runs through the primes.

Formula

a(n) = A036690(n) + 1.

a(n) = 1 + A008864(n)*A000040(n) = (A030078(n) - 1)/A006093(n). - Reinhard Zumkeller, Aug 06 2007

a(n) = sigma(prime(n)^2) = A000203(A000040(n)^2). - Zak Seidov, Feb 13 2016

a(n) = A000203(A001248(n)). - Michel Marcus, Feb 15 2016

Product_{n>=1} (1 - 1/a(n)) = zeta(3)/zeta(2) (A253905). - Amiram Eldar, Nov 07 2022

Example

a(3) = 31 because 5^2 + 5 + 1 = 31.

Maple

A060800:= n -> map (p -> p^(2)+p+1, ithprime(n)):
seq (A060800(n), n=1..41); # Jani Melik, Jan 25 2011

Mathematica

#^2 + # + 1&/@Prime[Range[200]] (* Vincenzo Librandi, Mar 20 2014 *)

Prog

(PARI) { n=0; forprime (p=2, prime(1000), write("b060800.txt", n++, " ", p^2 + p + 1); ) } \\ Harry J. Smith, Jul 13 2009
(Magma) [p^2+p+1: p in PrimesUpTo(200)]; // Vincenzo Librandi, Mar 20 2014

Crossrefs

Cf. A001248, A131991, A131992, A131993, A253905.

Cf. A008864, A000203. - Zak Seidov, Feb 13 2016

Sequence in context: A031158 A301683 A091431 * A272204 A107146 A201601

Adjacent sequences: A060797 A060798 A060799 * A060801 A060802 A060803

Keyword

nonn,easy

Author

Jason Earls, Apr 27 2001

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), May 03 2001

Status

approved