A341661 Primes p such that p^4 - 1 has fewer than 160 divisors.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 59, 61, 71, 79, 101

Offset: 1

Author

Jon E. Schoenfield, Feb 26 2021

Keywords

• nonn
• fini
• full

Comments

For all primes p > 101, p^4 - 1 has at least A309906(4)=160 divisors.

Examples

			      p =
   n  a(n)   p^4 - 1   factorization of p^4 - 1  tau(p^4 - 1)
  --  ----  ---------  ------------------------- ------------
   1    2          15  3 * 5                           4
   2    3          80  2^4 * 5                        10
   3    5         624  2^4 * 3 * 13                   20
   4    7        2400  2^5 * 3 * 5^2                  36
   5   11       14640  2^4 * 3 * 5 * 61               40
   6   13       28560  2^4 * 3 * 5 * 7 * 17           80
   7   17       83520  2^6 * 3^2 * 5 * 29             84
   8   19      130320  2^4 * 3^2 * 5 * 181            60
   9   23      279840  2^5 * 3 * 5 * 11 * 53          96
  10   29      707280  2^4 * 3 * 5 * 7 * 421          80
  11   31      923520  2^7 * 3 * 5 * 13 * 37         128
  12   37     1874160  2^4 * 3^2 * 5 * 19 * 137      120
  13   41     2825760  2^5 * 3 * 5 * 7 * 29^2        144
  14   59    12117360  2^4 * 3 * 5 * 29 * 1741        80
  15   61    13845840  2^4 * 3 * 5 * 31 * 1861        80
  16   71    25411680  2^5 * 3^2 * 5 * 7 * 2521      144
  17   79    38950080  2^6 * 3 * 5 * 13 * 3121       112
  18  101   104060400  2^4 * 3 * 5^2 * 17 * 5101     120
		

Crossrefs

Cf. A000005, A000040, A309906, A341656.

Programs

Mathematica

Select[Range[101], PrimeQ[#] && DivisorSigma[0, #^4 - 1] < 160 &] (* Amiram Eldar, Feb 26 2021 *)