A341660 Primes p such that p^2 - 1 has fewer than 32 divisors.

2, 3, 5, 7, 11, 13, 17, 19, 23, 31, 37, 47, 73

Offset: 1

Author

Jon E. Schoenfield, Feb 26 2021

Keywords

• nonn
• fini
• full

Comments

For all primes p > 73, p^2 - 1 has at least A309906(2)=32 divisors.

Examples

			      p =            factorization
   n  a(n)  p^2 - 1    of p^2 - 1    tau(p^2 - 1)
  --  ----  -------  --------------  ------------
   1    2        3   3                     2
   2    3        8   2^3                   4
   3    5       24   2^3 * 3               8
   4    7       48   2^4 * 3              10
   5   11      120   2^3 * 3 * 5          16
   6   13      168   2^3 * 3 * 7          16
   7   17      288   2^5 * 3^2            18
   8   19      360   2^3 * 3^2 * 5        24
   9   23      528   2^4 * 3 * 11         20
  10   31      960   2^6 * 3 * 5          28
  11   37     1368   2^3 * 3^2 * 19       24
  12   47     2208   2^5 * 3 * 23         24
  13   73     5328   2^4 * 3^2 * 37       30
		

Crossrefs

Cf. A000005, A000040, A309906, A341655, A341658.

Programs

Mathematica

Select[Range[100], PrimeQ[#] && DivisorSigma[0, #^2 - 1] < 32 &] (* Amiram Eldar, Feb 26 2021 *)