OFFSET
1,1
COMMENTS
For all primes p > 167, p^6 - 1 has at least 384 divisors.
EXAMPLE
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
MATHEMATICA
Select[Range[200], PrimeQ[#] && DivisorSigma[0, #^6 - 1] < 384 &] (* Amiram Eldar, Feb 27 2021 *)
CROSSREFS
KEYWORD
nonn,fini,full
AUTHOR
Jon E. Schoenfield, Feb 26 2021
STATUS
approved