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