A341667 Primes p such that p^6 - 1 has fewer than 384 divisors.

2, 3, 5, 7, 11, 13, 17, 19, 23, 41, 53, 71, 73, 167

Offset: 1

Author

Jon E. Schoenfield, Feb 26 2021

Keywords

• nonn
• fini
• full

Comments

For all primes p > 167, p^6 - 1 has at least 384 divisors.

Examples

			      p =
   n  a(n)      factorization of p^6 - 1       tau(p^6 - 1)
  --  ----  ---------------------------------  ------------
   1     2  3^2 * 7                                   6
   2     3  2^3 * 7 * 13                             16
   3     5  2^3 * 3^2 * 7 * 31                       48
   4     7  2^4 * 3^2 * 19 * 43                      60
   5    11  2^3 * 3^2 * 5 * 7 * 19 * 37             192
   6    13  2^3 * 3^2 * 7 * 61 * 157                 96
   7    17  2^5 * 3^3 * 7 * 13 * 307                192
   8    19  2^3 * 3^3 * 5 * 7^3 * 127               256
   9    23  2^4 * 3^2 * 7 * 11 * 13^2 * 79          360
  10    41  2^4 * 3^2 * 5 * 7 * 547 * 1723          240
  11    53  2^3 * 3^4 * 7 * 13 * 409 * 919          320
  12    71  2^4 * 3^3 * 5 * 7 * 1657 * 5113         320
  13    73  2^4 * 3^3 * 7 * 37 * 751 * 1801         320
  14   167  2^4 * 3^2 * 7 * 83 * 9241 * 28057       240
		

Crossrefs

Cf. A000005, A000040, A309906, A341657, A341666.

Programs

Mathematica

Select[Range[200], PrimeQ[#] && DivisorSigma[0, #^6 - 1] < 384 &] (* Amiram Eldar, Feb 27 2021 *)