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

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%I A341667 #13 Mar 04 2021 01:42:34
%S A341667 2,3,5,7,11,13,17,19,23,41,53,71,73,167
%N A341667 Primes p such that p^6 - 1 has fewer than 384 divisors.
%C A341667 For all primes p > 167, p^6 - 1 has at least 384 divisors.
%e A341667       p =
%e A341667    n  a(n)      factorization of p^6 - 1       tau(p^6 - 1)
%e A341667   --  ----  ---------------------------------  ------------
%e A341667    1     2  3^2 * 7                                   6
%e A341667    2     3  2^3 * 7 * 13                             16
%e A341667    3     5  2^3 * 3^2 * 7 * 31                       48
%e A341667    4     7  2^4 * 3^2 * 19 * 43                      60
%e A341667    5    11  2^3 * 3^2 * 5 * 7 * 19 * 37             192
%e A341667    6    13  2^3 * 3^2 * 7 * 61 * 157                 96
%e A341667    7    17  2^5 * 3^3 * 7 * 13 * 307                192
%e A341667    8    19  2^3 * 3^3 * 5 * 7^3 * 127               256
%e A341667    9    23  2^4 * 3^2 * 7 * 11 * 13^2 * 79          360
%e A341667   10    41  2^4 * 3^2 * 5 * 7 * 547 * 1723          240
%e A341667   11    53  2^3 * 3^4 * 7 * 13 * 409 * 919          320
%e A341667   12    71  2^4 * 3^3 * 5 * 7 * 1657 * 5113         320
%e A341667   13    73  2^4 * 3^3 * 7 * 37 * 751 * 1801         320
%e A341667   14   167  2^4 * 3^2 * 7 * 83 * 9241 * 28057       240
%t A341667 Select[Range[200], PrimeQ[#] && DivisorSigma[0, #^6 - 1] < 384 &] (* _Amiram Eldar_, Feb 27 2021 *)
%Y A341667 Cf. A000005, A000040, A309906, A341657, A341666.
%K A341667 nonn,fini,full
%O A341667 1,1
%A A341667 _Jon E. Schoenfield_, Feb 26 2021