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A084920 a(n) = (prime(n)-1)*(prime(n)+1). 33
3, 8, 24, 48, 120, 168, 288, 360, 528, 840, 960, 1368, 1680, 1848, 2208, 2808, 3480, 3720, 4488, 5040, 5328, 6240, 6888, 7920, 9408, 10200, 10608, 11448, 11880, 12768, 16128, 17160, 18768, 19320, 22200, 22800, 24648, 26568, 27888, 29928 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Squares of primes minus 1. - Wesley Ivan Hurt, Oct 11 2013
Integers k for which there exist exactly two positive integers b such that (k+1)/(b+1) is an integer. - Benedict W. J. Irwin, Jul 26 2016
LINKS
Barry Brent, On the Constant Terms of Certain Laurent Series, Preprints (2023) 2023061164.
Nik Lygeros and Olivier Rozier, A new solution to the equation tau(p) == 0 (mod p), J. Int. Seq. 13 (2010), Article 10.7.4.
FORMULA
a(n) = A006093(n) * A008864(n);
a(n) = A084921(n)*2, for n > 1; a(n) = A084922(n)*6, for n > 2.
Product_{n > 0} a(n)/A066872(n) = 2/5. a(n) = A001248(n) - 1. - R. J. Mathar, Feb 01 2009
a(n) = prime(n)^2 - 1 = A001248(n) - 1. - Vladimir Joseph Stephan Orlovsky, Oct 17 2009
a(n) ~ n^2*log(n)^2. - Ilya Gutkovskiy, Jul 28 2016
a(n) = (1/2) * Sum_{|k|<=2*sqrt(p)} k^2*H(4*p-k^2) where H() is the Hurwitz class number and p is n-th prime. - Seiichi Manyama, Dec 31 2017
a(n) = 24 * A024702(n) for n > 2. - Jianing Song, Apr 28 2019
Sum_{n>=1} 1/a(n) = A154945. - Amiram Eldar, Nov 09 2020
From Amiram Eldar, Nov 07 2022: (Start)
Product_{n>=1} (1 + 1/a(n)) = Pi^2/6 (A013661).
Product_{n>=1} (1 - 1/a(n)) = A065469. (End)
MAPLE
A084920:=n->ithprime(n)^2-1; seq(A084920(k), k=1..50); # Wesley Ivan Hurt, Oct 11 2013
MATHEMATICA
Table[Prime[n]^2 - 1, {n, 50}] (* Wesley Ivan Hurt, Oct 11 2013 *)
Prime[Range[50]]^2-1 (* Harvey P. Dale, Oct 02 2021 *)
PROG
(Haskell)
a084920 n = (p - 1) * (p + 1) where p = a000040 n
-- Reinhard Zumkeller, Aug 27 2013
(Magma) [p^2-1: p in PrimesUpTo(200)]; // Vincenzo Librandi, Mar 30 2015
(Sage) [(p-1)*(p+1) for p in primes(200)] # Bruno Berselli, Mar 30 2015
(PARI) a(n) = (prime(n)-1)*(prime(n)+1); \\ Michel Marcus, Jul 28 2016
CROSSREFS
Sequence in context: A280190 A037450 A081990 * A323278 A026556 A096001
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, Jun 11 2003
STATUS
approved

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Last modified February 27 07:56 EST 2024. Contains 370367 sequences. (Running on oeis4.)