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A341655 a(n) is the number of divisors of prime(n)^2 - 1.

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%I A341655 #14 Mar 04 2021 01:43:43
%S A341655 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 A341655 42,48,40,32,64,48,54,64,40,64,48,60,32,40,40,32,48,96,64,32,72,90,64,
%U A341655 56,32,64,60,96,72,96,40,40,64,96,32,80,32,48,96,80,40,32
%N A341655 a(n) is the number of divisors of prime(n)^2 - 1.
%C A341655 a(n) >= A309906(2) = 32 for n > 21.
%F A341655 a(n) = A000005(A000040(n)^2 - 1) = A000005(A084920(n)).
%e A341655         p =                factorization
%e A341655    n  prime(n)  p^2 - 1      of p^2 - 1      a(n)
%e A341655   --  --------  -------  ------------------  ----
%e A341655    1      2         3    3                     2
%e A341655    2      3         8    2^3                   4
%e A341655    3      5        24    2^3 * 3               8
%e A341655    4      7        48    2^4 * 3              10
%e A341655    5     11       120    2^3 * 3 * 5          16
%e A341655    6     13       168    2^3 * 3 * 7          16
%e A341655    7     17       288    2^5 * 3^2            18
%e A341655    8     19       360    2^3 * 3^2 * 5        24
%e A341655    9     23       528    2^4 * 3 * 11         20
%e A341655   10     29       840    2^3 * 3 * 5 * 7      32
%e A341655   11     31       960    2^6 * 3 * 5          28
%e A341655   12     37      1368    2^3 * 3^2 * 19       24
%e A341655   13     41      1680    2^4 * 3 * 5 * 7      40
%e A341655   14     43      1848    2^3 * 3 * 7 * 11     32
%e A341655   15     47      2208    2^5 * 3 * 23         24
%e A341655   16     53      2808    2^3 * 3^3 * 13       32
%e A341655   17     59      3480    2^3 * 3 * 5 * 29     32
%e A341655   18     61      3720    2^3 * 3 * 5 * 31     32
%e A341655   19     67      4488    2^3 * 3 * 11 * 17    32
%e A341655   20     71      5040    2^4 * 3^2 * 5 * 7    60
%e A341655   21     73      5328    2^4 * 3^2 * 37       30
%e A341655   22     79      6240    2^5 * 3 * 5 * 13     48
%e A341655   23     83      6888    2^3 * 3 * 7 * 41     32
%e A341655   24     89      7920    2^4 * 3^2 * 5 * 11   60
%t A341655 Table[DivisorSigma[0,Prime[n]^2-1],{n,66}] (* _Stefano Spezia_, Feb 25 2021 *)
%o A341655 (PARI) a(n) = numdiv(prime(n)^2-1); \\ _Michel Marcus_, Feb 25 2021
%Y A341655 Cf. A000005, A000040, A084920, A309906.
%K A341655 nonn
%O A341655 1,1
%A A341655 _Jon E. Schoenfield_, Feb 25 2021