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a(n) is the number of divisors of prime(n)^8 - 1.
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%I #20 Mar 04 2021 01:43:03

%S 8,24,48,84,96,192,192,288,224,192,576,576,672,2304,1024,768,768,192,

%T 768,336,672,1024,3072,1344,864,576,448,1152,1536,512,2112,768,1792,

%U 768,1152,1344,2304,960,896,1536,1728,1152,2560,1280,1728,504,1536,2304,1536

%N a(n) is the number of divisors of prime(n)^8 - 1.

%C a(n) >= 384 for n > 20.

%H Robert Israel, <a href="/A342062/b342062.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A000005(A000040(n)^8 - 1).

%e n prime(n) factorization of prime(n)^8 - 1 a(n)

%e -- -------- --------------------------------------- ----

%e 1 2 3 * 5 * 17 8

%e 2 3 2^5 * 5 * 41 24

%e 3 5 2^5 * 3 * 13 * 313 48

%e 4 7 2^6 * 3 * 5^2 * 1201 84

%e 5 11 2^5 * 3 * 5 * 61 * 7321 96

%e 6 13 2^5 * 3 * 5 * 7 * 17 * 14281 192

%e 7 17 2^7 * 3^2 * 5 * 29 * 41761 192

%e 8 19 2^5 * 3^2 * 5 * 17 * 181 * 3833 288

%e 9 23 2^6 * 3 * 5 * 11 * 53 * 139921 224

%e 10 29 2^5 * 3 * 5 * 7 * 421 * 353641 192

%e 11 31 2^8 * 3 * 5 * 13 * 37 * 409 * 1129 576

%e 12 37 2^5 * 3^2 * 5 * 19 * 89 * 137 * 10529 576

%e 13 41 2^6 * 3 * 5 * 7 * 29^2 * 137 * 10313 672

%e ...

%e 20 71 2^6 * 3^2 * 5 * 7 * 2521 * 12705841 336

%p f:= n -> numtheory:-tau(ithprime(n)^8-1):

%p map(f, [$1..100]); # _Robert Israel_, Feb 28 2021

%t a[n_] := DivisorSigma[0, Prime[n]^8 - 1]; Array[a, 50] (* _Amiram Eldar_, Feb 27 2021 *)

%o (PARI) a(n) = numdiv(prime(n)^8-1); \\ _Michel Marcus_, Feb 27 2021

%Y Cf. A000005, A000040, A309906, A342063, A342064.

%K nonn

%O 1,1

%A _Jon E. Schoenfield_, Feb 27 2021