A359069 Smallest prime p such that p^(2n-1) - 1 is the product of 2n-1 distinct primes.

3, 59, 47, 79, 347, 6343, 56711, 4523

Offset: 1

Author

Kevin P. Thompson, Dec 15 2022

Keywords

• nonn
• hard
• more

Comments

a(9) > 113500.

a(9) > 1000000, a(10) > 237000, a(11) > 209021. - Sean A. Irvine, Jan 10 2023

a(n)-1 is squarefree for all n. - Chai Wah Wu, Jan 30 2023

Examples

			a(3) = 47 since 47^(2*3-1) - 1 = 229345006 = 2*11*23*31*14621 is the product of 5 distinct primes and 47 is the smallest prime number with this property.
		

Crossrefs

Cf. A001597, A005117, A045542, A280005, A359070.

Programs

PARI

isok(p, n) = my(f=factor(p^(2*n-1)-1)); issquarefree(f) && (omega(f) == 2*n-1);
a(n) = my(p=2); while (!isok(p, n), p=nextprime(p+1)); p; \\ Michel Marcus, Dec 15 2022