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

Author

Jason Earls, Apr 27 2001

Keywords

• nonn
• easy

Comments

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

Examples

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

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.

Crossrefs

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

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

Programs

Magma

[p^2+p+1: p in PrimesUpTo(200)]; // Vincenzo Librandi, Mar 20 2014

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 *)

PARI

{ n=0; forprime (p=2, prime(1000), write("b060800.txt", n++, " ", p^2 + p + 1); ) } \\ Harry J. Smith, Jul 13 2009

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

Extensions

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