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A341664 a(n) is the number of divisors of prime(n)^5 - 1.

%I A341664 #15 Mar 04 2021 01:42:48
%S A341664 2,6,12,8,12,12,10,24,8,12,48,72,24,16,32,48,64,72,32,96,24,16,8,64,
%T A341664 96,96,32,16,96,80,24,48,64,32,48,32,96,160,32,24,16,108,96,28,72,48,
%U A341664 96,128,8,48,32,16,120,60,36,8,36,96,24,192,64,24,96,48,64,48
%N A341664 a(n) is the number of divisors of prime(n)^5 - 1.
%C A341664 a(n) >= A309906(5) = 8 for n > 2.
%F A341664 a(n) = A000005(A000040(n)^5 - 1).
%e A341664        p =                factorization
%e A341664   n  prime(n)  p^5 - 1      of p^5 - 1      a(n)
%e A341664   -  --------  -------  ------------------  ----
%e A341664   1      2          31  31                    2
%e A341664   2      3         242  2 * 11^2              6
%e A341664   3      5        3124  2^2 * 11 * 71        12
%e A341664   4      7       16806  2 * 3 * 2801          8
%e A341664   5     11      161050  2 * 5^2 * 3221       12
%e A341664   6     13      371292  2^2 * 3 * 30941      12
%e A341664   7     17     1419856  2^4 * 88741          10
%e A341664   8     19     2476098  2 * 3^2 * 151 * 911  24
%e A341664   9     23     6436342  2 * 11 * 292561       8
%e A341664   ...
%t A341664 a[n_] := DivisorSigma[0, Prime[n]^5 - 1]; Array[a, 50] (* _Amiram Eldar_, Feb 26 2021 *)
%o A341664 (PARI) a(n) = numdiv(prime(n)^5-1); \\ _Michel Marcus_, Feb 26 2021
%Y A341664 Cf. A000005, A000040, A309906, A341665.
%K A341664 nonn
%O A341664 1,1
%A A341664 _Jon E. Schoenfield_, Feb 26 2021