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A341656 a(n) is the number of divisors of prime(n)^4 - 1. 5
4, 10, 20, 36, 40, 80, 84, 60, 96, 80, 128, 120, 144, 240, 224, 160, 80, 80, 160, 144, 288, 112, 320, 288, 192, 120, 192, 240, 320, 224, 240, 160, 192, 160, 240, 288, 480, 200, 192, 320, 240, 240, 576, 288, 360, 216, 320, 256, 160, 320, 576, 560, 336, 720, 264 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) >= A309906(4) = 160 for n > 26.

LINKS

Table of n, a(n) for n=1..55.

FORMULA

a(n) = A000005(A000040(n)^4 - 1).

EXAMPLE

        p =                       factorization

   n  prime(n)  p^4 - 1             of p^4 - 1            a(n)

  --  -------- ---------  ------------------------------  ----

   1      2           15  3 * 5                              4

   2      3           80  2^4 * 5                           10

   3      5          624  2^4 * 3 * 13                      20

   4      7         2400  2^5 * 3 * 5^2                     36

   5     11        14640  2^4 * 3 * 5 * 61                  40

   6     13        28560  2^4 * 3 * 5 * 7 * 17              80

   7     17        83520  2^6 * 3^2 * 5 * 29                84

   8     19       130320  2^4 * 3^2 * 5 * 181               60

   9     23       279840  2^5 * 3 * 5 * 11 * 53             96

  10     29       707280  2^4 * 3 * 5 * 7 * 421             80

  11     31       923520  2^7 * 3 * 5 * 13 * 37            128

  12     37      1874160  2^4 * 3^2 * 5 * 19 * 137         120

  13     41      2825760  2^5 * 3 * 5 * 7 * 29^2           144

  14     43      3418800  2^4 * 3 * 5^2 * 7 * 11 * 37      240

  15     47      4879680  2^6 * 3 * 5 * 13 * 17 * 23       224

  16     53      7890480  2^4 * 3^3 * 5 * 13 * 281         160

  17     59     12117360  2^4 * 3 * 5 * 29 * 1741           80

  18     61     13845840  2^4 * 3 * 5 * 31 * 1861           80

  19     67     20151120  2^4 * 3 * 5 * 11 * 17 * 449      160

  20     71     25411680  2^5 * 3^2 * 5 * 7 * 2521         144

  21     73     28398240  2^5 * 3^2 * 5 * 13 * 37 * 41     288

  22     79     38950080  2^6 * 3 * 5 * 13 * 3121          112

  23     83     47458320  2^4 * 3 * 5 * 7 * 13 * 41 * 53   320

  24     89     62742240  2^5 * 3^2 * 5 * 11 * 17 * 233    288

  25     97     88529280  2^7 * 3 * 5 * 7^2 * 941          192

  26    101    104060400  2^4 * 3 * 5^2 * 17 * 5101        120

MATHEMATICA

a[n_] := DivisorSigma[0, Prime[n]^4 - 1]; Array[a, 50] (* Amiram Eldar, Feb 25 2021 *)

PROG

(PARI) a(n) = numdiv(prime(n)^4-1); \\ Michel Marcus, Feb 25 2021

(Python)

from sympy import prime, divisor_count

def A341656(n): return divisor_count(prime(n)**4-1) # Chai Wah Wu, Feb 25 2021

CROSSREFS

Cf. A000005, A000040, A309906.

Sequence in context: A134987 A261636 A058539 * A008112 A301153 A301008

Adjacent sequences:  A341653 A341654 A341655 * A341657 A341658 A341659

KEYWORD

nonn

AUTHOR

Jon E. Schoenfield, Feb 25 2021

STATUS

approved

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Last modified May 11 19:29 EDT 2021. Contains 343808 sequences. (Running on oeis4.)