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A341668 a(n) is the number of divisors of prime(n)^7 - 1. 1
2, 4, 6, 16, 16, 12, 10, 24, 16, 18, 16, 36, 32, 48, 16, 24, 64, 24, 32, 48, 24, 128, 16, 16, 96, 36, 64, 32, 96, 60, 144, 64, 32, 64, 12, 48, 48, 20, 16, 24, 16, 144, 128, 56, 96, 192, 96, 128, 32, 48, 64, 96, 80, 16, 72, 32, 192, 64, 96, 192, 32, 48, 48, 64 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) >= A309906(7) = 8 for n > 3.

LINKS

Table of n, a(n) for n=1..64.

FORMULA

a(n) = A000005(A000040(n)^7 - 1).

EXAMPLE

       p =                     factorization

  n  prime(n)   p^7 - 1          of p^7 - 1       a(n)

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

  1      2            127  127                      2

  2      3           2186  2 * 1093                 4

  3      5          78124  2^2 * 19531              6

  4      7         823542  2 * 3 * 29 * 4733       16

  5     11       19487170  2 * 5 * 43 * 45319      16

  6     13       62748516  2^2 * 3 * 5229043       12

  7     17      410338672  2^4 * 25646167          10

  8     19      893871738  2 * 3^2 * 701 * 70841   24

  9     23     3404825446  2 * 11 * 29 * 5336717   16

MATHEMATICA

a[n_] := DivisorSigma[0, Prime[n]^7 - 1]; Array[a, 50] (* Amiram Eldar, Feb 27 2021 *)

PROG

(PARI) a(n) = numdiv(prime(n)^7-1); \\ Michel Marcus, Feb 27 2021

CROSSREFS

Cf. A000005, A000040, A309906, A341669.

Sequence in context: A099315 A005179 A037019 * A326782 A096174 A096173

Adjacent sequences:  A341665 A341666 A341667 * A341669 A341670 A341671

KEYWORD

nonn

AUTHOR

Jon E. Schoenfield, Feb 26 2021

STATUS

approved

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Last modified April 12 01:36 EDT 2021. Contains 342912 sequences. (Running on oeis4.)