A341668 a(n) is the number of divisors of prime(n)^7 - 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

Offset: 1

Author

Jon E. Schoenfield, Feb 26 2021

Keywords

• nonn

Comments

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

Examples

			       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
		

Crossrefs

Cf. A000005, A000040, A309906, A341669.

Programs

Mathematica

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

PARI

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

Formula

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