A005722 a(n) = (prime(n) - 1)^2.

1, 4, 16, 36, 100, 144, 256, 324, 484, 784, 900, 1296, 1600, 1764, 2116, 2704, 3364, 3600, 4356, 4900, 5184, 6084, 6724, 7744, 9216, 10000, 10404, 11236, 11664, 12544, 15876, 16900, 18496, 19044, 21904, 22500, 24336, 26244, 27556, 29584, 31684, 32400, 36100

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Richard K. Guy, Letter to N. J. A. Sloane, 1987.

Formula

a(n) = A192134(A095874(A001248(n))) - 1. - Reinhard Zumkeller, Jun 26 2011

a(n) = A006093(n)^2. - Wesley Ivan Hurt, Mar 27 2014

Sum_{n>=1} 1/a(n) = A086242. - Amiram Eldar, Nov 09 2020

From Amiram Eldar, Jan 23 2021: (Start)

Product_{n>=1} (1 + 1/a(n)) = A065485.

Product_{n>=2} (1 - 1/a(n)) = A005597. (End)

Maple

A005722:=n->(ithprime(n)-1)^2; seq(A005722(n), n=1..40); # Wesley Ivan Hurt, Mar 27 2014

Mathematica

Table[(Prime[n] - 1)^2, {n, 40}] (* Vincenzo Librandi, Mar 27 2014 *)

Prog

(Magma) [(p-1)^2: p in PrimesUpTo(200)]; // Vincenzo Librandi, Mar 27 2014
(PARI) a(n) = (prime(n) - 1)^2; \\ Michel Marcus, Nov 09 2020

Crossrefs

Cf. A001248, A005597, A006093, A065485, A086242, A095874, A192134.

Sequence in context: A207069 A207436 A189145 * A372635 A075408 A206981

Adjacent sequences: A005719 A005720 A005721 * A005723 A005724 A005725

Keyword

nonn,easy

Author

Scorpion(AT)aol.com

Status

approved