OFFSET
1,1
COMMENTS
For all primes p > 101, p^4 - 1 has at least A309906(4)=160 divisors.
EXAMPLE
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
MATHEMATICA
Select[Range[101], PrimeQ[#] && DivisorSigma[0, #^4 - 1] < 160 &] (* Amiram Eldar, Feb 26 2021 *)
CROSSREFS
KEYWORD
nonn,fini,full
AUTHOR
Jon E. Schoenfield, Feb 26 2021
STATUS
approved