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A341668 a(n) is the number of divisors of prime(n)^7 - 1.

%I A341668 #13 Mar 04 2021 01:42:31
%S A341668 2,4,6,16,16,12,10,24,16,18,16,36,32,48,16,24,64,24,32,48,24,128,16,
%T A341668 16,96,36,64,32,96,60,144,64,32,64,12,48,48,20,16,24,16,144,128,56,96,
%U A341668 192,96,128,32,48,64,96,80,16,72,32,192,64,96,192,32,48,48,64
%N A341668 a(n) is the number of divisors of prime(n)^7 - 1.
%C A341668 a(n) >= A309906(7) = 8 for n > 3.
%F A341668 a(n) = A000005(A000040(n)^7 - 1).
%e A341668        p =                     factorization
%e A341668   n  prime(n)   p^7 - 1          of p^7 - 1       a(n)
%e A341668   -  --------  ----------  ---------------------  ----
%e A341668   1      2            127  127                      2
%e A341668   2      3           2186  2 * 1093                 4
%e A341668   3      5          78124  2^2 * 19531              6
%e A341668   4      7         823542  2 * 3 * 29 * 4733       16
%e A341668   5     11       19487170  2 * 5 * 43 * 45319      16
%e A341668   6     13       62748516  2^2 * 3 * 5229043       12
%e A341668   7     17      410338672  2^4 * 25646167          10
%e A341668   8     19      893871738  2 * 3^2 * 701 * 70841   24
%e A341668   9     23     3404825446  2 * 11 * 29 * 5336717   16
%t A341668 a[n_] := DivisorSigma[0, Prime[n]^7 - 1]; Array[a, 50] (* _Amiram Eldar_, Feb 27 2021 *)
%o A341668 (PARI) a(n) = numdiv(prime(n)^7-1); \\ _Michel Marcus_, Feb 27 2021
%Y A341668 Cf. A000005, A000040, A309906, A341669.
%K A341668 nonn
%O A341668 1,1
%A A341668 _Jon E. Schoenfield_, Feb 26 2021