|
%I #12 Mar 04 2021 01:43:25
%S 2,3,5,7,11,13,17,19,23,31,37,47,73
%N Primes p such that p^2 - 1 has fewer than 32 divisors.
%C For all primes p > 73, p^2 - 1 has at least A309906(2)=32 divisors.
%e p = factorization
%e n a(n) p^2 - 1 of p^2 - 1 tau(p^2 - 1)
%e -- ---- ------- -------------- ------------
%e 1 2 3 3 2
%e 2 3 8 2^3 4
%e 3 5 24 2^3 * 3 8
%e 4 7 48 2^4 * 3 10
%e 5 11 120 2^3 * 3 * 5 16
%e 6 13 168 2^3 * 3 * 7 16
%e 7 17 288 2^5 * 3^2 18
%e 8 19 360 2^3 * 3^2 * 5 24
%e 9 23 528 2^4 * 3 * 11 20
%e 10 31 960 2^6 * 3 * 5 28
%e 11 37 1368 2^3 * 3^2 * 19 24
%e 12 47 2208 2^5 * 3 * 23 24
%e 13 73 5328 2^4 * 3^2 * 37 30
%t Select[Range[100], PrimeQ[#] && DivisorSigma[0, #^2 - 1] < 32 &] (* _Amiram Eldar_, Feb 26 2021 *)
%Y Cf. A000005, A000040, A309906, A341655, A341658.
%K nonn,fini,full
%O 1,1
%A _Jon E. Schoenfield_, Feb 26 2021
| 