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%I #14 Mar 04 2021 01:43:43
%S 2,4,8,10,16,16,18,24,20,32,28,24,40,32,24,32,32,32,32,60,30,48,32,60,
%T 42,48,40,32,64,48,54,64,40,64,48,60,32,40,40,32,48,96,64,32,72,90,64,
%U 56,32,64,60,96,72,96,40,40,64,96,32,80,32,48,96,80,40,32
%N a(n) is the number of divisors of prime(n)^2 - 1.
%C a(n) >= A309906(2) = 32 for n > 21.
%F a(n) = A000005(A000040(n)^2 - 1) = A000005(A084920(n)).
%e p = factorization
%e n prime(n) p^2 - 1 of p^2 - 1 a(n)
%e -- -------- ------- ------------------ ----
%e 1 2 3 3 2
%e 2 3 8 2^3 4
%e 3 5 24 2^3 * 3 8
%e 4 7 48 2^4 * 3 10
%e 5 11 120 2^3 * 3 * 5 16
%e 6 13 168 2^3 * 3 * 7 16
%e 7 17 288 2^5 * 3^2 18
%e 8 19 360 2^3 * 3^2 * 5 24
%e 9 23 528 2^4 * 3 * 11 20
%e 10 29 840 2^3 * 3 * 5 * 7 32
%e 11 31 960 2^6 * 3 * 5 28
%e 12 37 1368 2^3 * 3^2 * 19 24
%e 13 41 1680 2^4 * 3 * 5 * 7 40
%e 14 43 1848 2^3 * 3 * 7 * 11 32
%e 15 47 2208 2^5 * 3 * 23 24
%e 16 53 2808 2^3 * 3^3 * 13 32
%e 17 59 3480 2^3 * 3 * 5 * 29 32
%e 18 61 3720 2^3 * 3 * 5 * 31 32
%e 19 67 4488 2^3 * 3 * 11 * 17 32
%e 20 71 5040 2^4 * 3^2 * 5 * 7 60
%e 21 73 5328 2^4 * 3^2 * 37 30
%e 22 79 6240 2^5 * 3 * 5 * 13 48
%e 23 83 6888 2^3 * 3 * 7 * 41 32
%e 24 89 7920 2^4 * 3^2 * 5 * 11 60
%t Table[DivisorSigma[0,Prime[n]^2-1],{n,66}] (* _Stefano Spezia_, Feb 25 2021 *)
%o (PARI) a(n) = numdiv(prime(n)^2-1); \\ _Michel Marcus_, Feb 25 2021
%Y Cf. A000005, A000040, A084920, A309906.
%K nonn
%O 1,1
%A _Jon E. Schoenfield_, Feb 25 2021
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