mersenneforum.org - View Single Post - Question about number of the form 2^n + 1

jshort · 2020-10-03, 23:11

Let $a_{n}$ be the nth Highly Composite Integer* and $b_{n} = lcm(2^{a_{1}} + 1, 2^{a_{2}} + 1, ...,2^{a_{n}} + 1)$ . If $c_{n} = \frac{2^{a_{n}} + 1}{gcd(2^{a_{n}} + 1,b_{n-1})}$ , will $c_{n}$ always be equal to either 1 or a prime number?

*https://en.wikipedia.org/wiki/Highly...n%20the%20OEIS).

2020-10-03, 23:11	#1
jshort "James Short" Mar 2019 Canada 17 Posts	Question about number of the form 2^n + 1 Let $a_{n}$ be the nth Highly Composite Integer* and $b_{n} = lcm(2^{a_{1}} + 1, 2^{a_{2}} + 1, ...,2^{a_{n}} + 1)$ . If $c_{n} = \frac{2^{a_{n}} + 1}{gcd(2^{a_{n}} + 1,b_{n-1})}$ , will $c_{n}$ always be equal to either 1 or a prime number? *https://en.wikipedia.org/wiki/Highly...n%20the%20OEIS).