A359069 - OEIS

%I #20 Jan 31 2023 08:32:34

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

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

%C a(9) > 113500.

%C a(9) > 1000000, a(10) > 237000, a(11) > 209021. - _Sean A. Irvine_, Jan 10 2023

%C a(n)-1 is squarefree for all n. - _Chai Wah Wu_, Jan 30 2023

%e 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.

%o (PARI) isok(p, n) = my(f=factor(p^(2*n-1)-1)); issquarefree(f) && (omega(f) == 2*n-1);

%o a(n) = my(p=2); while (!isok(p, n), p=nextprime(p+1)); p; \\ _Michel Marcus_, Dec 15 2022

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

%K nonn,hard,more

%O 1,1

%A _Kevin P. Thompson_, Dec 15 2022