A341660 - OEIS

%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