A341664 a(n) is the number of divisors of prime(n)^5 - 1.

2, 6, 12, 8, 12, 12, 10, 24, 8, 12, 48, 72, 24, 16, 32, 48, 64, 72, 32, 96, 24, 16, 8, 64, 96, 96, 32, 16, 96, 80, 24, 48, 64, 32, 48, 32, 96, 160, 32, 24, 16, 108, 96, 28, 72, 48, 96, 128, 8, 48, 32, 16, 120, 60, 36, 8, 36, 96, 24, 192, 64, 24, 96, 48, 64, 48

Offset

1,1

Comments

a(n) >= A309906(5) = 8 for n > 2.

Links

Table of n, a(n) for n=1..66.

Formula

a(n) = A000005(A000040(n)^5 - 1).

Example

       p =                factorization
  n  prime(n)  p^5 - 1      of p^5 - 1      a(n)
  -  --------  -------  ------------------  ----
  1      2          31  31                    2
  2      3         242  2 * 11^2              6
  3      5        3124  2^2 * 11 * 71        12
  4      7       16806  2 * 3 * 2801          8
  5     11      161050  2 * 5^2 * 3221       12
  6     13      371292  2^2 * 3 * 30941      12
  7     17     1419856  2^4 * 88741          10
  8     19     2476098  2 * 3^2 * 151 * 911  24
  9     23     6436342  2 * 11 * 292561       8
  ...

Mathematica

a[n_] := DivisorSigma[0, Prime[n]^5 - 1]; Array[a, 50] (* Amiram Eldar, Feb 26 2021 *)

Prog

(PARI) a(n) = numdiv(prime(n)^5-1); \\ Michel Marcus, Feb 26 2021

Crossrefs

Cf. A000005, A000040, A309906, A341665.

Sequence in context: A338376 A113540 A111658 * A105692 A107647 A210842

Adjacent sequences: A341661 A341662 A341663 * A341665 A341666 A341667

Keyword

nonn

Author

Jon E. Schoenfield, Feb 26 2021

Status

approved