%I #14 Mar 04 2021 01:43:39
%S 2,3,5,7,11,13,17,19,23,29,31,37,41,59,61,71,79,101
%N Primes p such that p^4 - 1 has fewer than 160 divisors.
%C For all primes p > 101, p^4 - 1 has at least A309906(4)=160 divisors.
%e p =
%e n a(n) p^4 - 1 factorization of p^4 - 1 tau(p^4 - 1)
%e -- ---- --------- ------------------------- ------------
%e 1 2 15 3 * 5 4
%e 2 3 80 2^4 * 5 10
%e 3 5 624 2^4 * 3 * 13 20
%e 4 7 2400 2^5 * 3 * 5^2 36
%e 5 11 14640 2^4 * 3 * 5 * 61 40
%e 6 13 28560 2^4 * 3 * 5 * 7 * 17 80
%e 7 17 83520 2^6 * 3^2 * 5 * 29 84
%e 8 19 130320 2^4 * 3^2 * 5 * 181 60
%e 9 23 279840 2^5 * 3 * 5 * 11 * 53 96
%e 10 29 707280 2^4 * 3 * 5 * 7 * 421 80
%e 11 31 923520 2^7 * 3 * 5 * 13 * 37 128
%e 12 37 1874160 2^4 * 3^2 * 5 * 19 * 137 120
%e 13 41 2825760 2^5 * 3 * 5 * 7 * 29^2 144
%e 14 59 12117360 2^4 * 3 * 5 * 29 * 1741 80
%e 15 61 13845840 2^4 * 3 * 5 * 31 * 1861 80
%e 16 71 25411680 2^5 * 3^2 * 5 * 7 * 2521 144
%e 17 79 38950080 2^6 * 3 * 5 * 13 * 3121 112
%e 18 101 104060400 2^4 * 3 * 5^2 * 17 * 5101 120
%t Select[Range[101], PrimeQ[#] && DivisorSigma[0, #^4 - 1] < 160 &] (* _Amiram Eldar_, Feb 26 2021 *)
%Y Cf. A000005, A000040, A309906, A341656.
%K nonn,fini,full
%O 1,1
%A _Jon E. Schoenfield_, Feb 26 2021
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