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A341656 a(n) is the number of divisors of prime(n)^4 - 1.

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%I A341656 #15 Mar 04 2021 02:30:58
%S A341656 4,10,20,36,40,80,84,60,96,80,128,120,144,240,224,160,80,80,160,144,
%T A341656 288,112,320,288,192,120,192,240,320,224,240,160,192,160,240,288,480,
%U A341656 200,192,320,240,240,576,288,360,216,320,256,160,320,576,560,336,720,264
%N A341656 a(n) is the number of divisors of prime(n)^4 - 1.
%C A341656 a(n) >= A309906(4) = 160 for n > 26.
%F A341656 a(n) = A000005(A000040(n)^4 - 1).
%e A341656         p =                       factorization
%e A341656    n  prime(n)  p^4 - 1             of p^4 - 1            a(n)
%e A341656   --  -------- ---------  ------------------------------  ----
%e A341656    1      2           15  3 * 5                              4
%e A341656    2      3           80  2^4 * 5                           10
%e A341656    3      5          624  2^4 * 3 * 13                      20
%e A341656    4      7         2400  2^5 * 3 * 5^2                     36
%e A341656    5     11        14640  2^4 * 3 * 5 * 61                  40
%e A341656    6     13        28560  2^4 * 3 * 5 * 7 * 17              80
%e A341656    7     17        83520  2^6 * 3^2 * 5 * 29                84
%e A341656    8     19       130320  2^4 * 3^2 * 5 * 181               60
%e A341656    9     23       279840  2^5 * 3 * 5 * 11 * 53             96
%e A341656   10     29       707280  2^4 * 3 * 5 * 7 * 421             80
%e A341656   11     31       923520  2^7 * 3 * 5 * 13 * 37            128
%e A341656   12     37      1874160  2^4 * 3^2 * 5 * 19 * 137         120
%e A341656   13     41      2825760  2^5 * 3 * 5 * 7 * 29^2           144
%e A341656   14     43      3418800  2^4 * 3 * 5^2 * 7 * 11 * 37      240
%e A341656   15     47      4879680  2^6 * 3 * 5 * 13 * 17 * 23       224
%e A341656   16     53      7890480  2^4 * 3^3 * 5 * 13 * 281         160
%e A341656   17     59     12117360  2^4 * 3 * 5 * 29 * 1741           80
%e A341656   18     61     13845840  2^4 * 3 * 5 * 31 * 1861           80
%e A341656   19     67     20151120  2^4 * 3 * 5 * 11 * 17 * 449      160
%e A341656   20     71     25411680  2^5 * 3^2 * 5 * 7 * 2521         144
%e A341656   21     73     28398240  2^5 * 3^2 * 5 * 13 * 37 * 41     288
%e A341656   22     79     38950080  2^6 * 3 * 5 * 13 * 3121          112
%e A341656   23     83     47458320  2^4 * 3 * 5 * 7 * 13 * 41 * 53   320
%e A341656   24     89     62742240  2^5 * 3^2 * 5 * 11 * 17 * 233    288
%e A341656   25     97     88529280  2^7 * 3 * 5 * 7^2 * 941          192
%e A341656   26    101    104060400  2^4 * 3 * 5^2 * 17 * 5101        120
%t A341656 a[n_] := DivisorSigma[0, Prime[n]^4 - 1]; Array[a, 50] (* _Amiram Eldar_, Feb 25 2021 *)
%o A341656 (PARI) a(n) = numdiv(prime(n)^4-1); \\ _Michel Marcus_, Feb 25 2021
%o A341656 (Python)
%o A341656 from sympy import prime, divisor_count
%o A341656 def A341656(n): return divisor_count(prime(n)**4-1) # _Chai Wah Wu_, Feb 25 2021
%Y A341656 Cf. A000005, A000040, A309906.
%K A341656 nonn
%O A341656 1,1
%A A341656 _Jon E. Schoenfield_, Feb 25 2021