A366818 Let p = A000043(n) be the n-th Mersenne exponent, then a(n) = ((2^p-1)^2-1)/p.

4, 16, 192, 2304, 5160960, 1010565120, 14467203072, 148764064972013568, 87162491526879729295140036437606400, 4304762755241260838085244444377946703587691074682880, 246056756234946697892331840382404519263272106760845744463151104, 227937183538024006739312962615527377661237903932985846822055286571232395264

Offset: 1

Author

Jianing Song, Oct 24 2023

Keywords

• nonn

Comments

a(n) is the largest k such that 2 is a k-th power in the finite field F_{2^p-1}(i), where i^2 = -1.

Examples

			In F_9 = F_3(i), we have 2 = (1+i)^2.
Jn F_49 = F_7(i), we have 2 = (3+i)^16.
In F_961 = F_31(i), we have 2 = (5+4*i)^192.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..15

Crossrefs

Cf. A000043, A000668.

Programs

PARI

A366818(lim) = my(q); forprime(p=2, lim, if(isprime(q=2^p-1), print1((q^2-1)/p, ", ")))