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A060800
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a(n) = p^2 + p + 1 where p runs through the primes.
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21
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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
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OFFSET
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1,1
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COMMENTS
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Terms are divisible by 3 iff p is of the form 6*m+1 (A002476). - Michel Marcus, Jan 15 2017
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LINKS
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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, 2018.
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FORMULA
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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
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EXAMPLE
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a(3)=31 because 5^2 + 5 + 1 = 31.
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MAPLE
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A060800:= n -> map (p -> p^(2)+p+1, ithprime(n)):
seq (A060800(n), n=1..41); # Jani Melik, Jan 25 2011
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MATHEMATICA
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#^2 + # + 1&/@Prime[Range[200]] (* Vincenzo Librandi, Mar 20 2014 *)
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PROG
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(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
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CROSSREFS
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Cf. A001248, A131991, A131992, A131993.
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
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KEYWORD
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nonn,easy
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AUTHOR
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Jason Earls, Apr 27 2001
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), May 03 2001
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STATUS
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approved
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