A046801 Number of divisors of 2^n-1.

1, 2, 2, 4, 2, 6, 2, 8, 4, 8, 4, 24, 2, 8, 8, 16, 2, 32, 2, 48, 12, 16, 4, 96, 8, 8, 8, 64, 8, 96, 2, 32, 16, 8, 16, 512, 4, 8, 16, 192, 4, 144, 8, 128, 64, 16, 8, 768, 4, 128, 32, 128, 8, 160, 64, 256, 16, 64, 4, 4608, 2, 8, 96, 128, 8, 384, 4, 128, 16, 512, 8, 8192, 8, 32, 128

Offset

1,2

Comments

a(0) cannot be defined because 0's divisors are an infinite set (every number is a divisor of 0.)

Links

Amiram Eldar, Table of n, a(n) for n = 1..1206 (terms 1..500 from T. D. Noe)

Example

a(120) = 73728 since 2^120-1 has that many divisors.

Maple

a:= n-> numtheory[tau](2^n-1):
seq(a(n), n=1..80);  # Alois P. Heinz, Aug 23 2021

Mathematica

Table[DivisorSigma[0, 2^n - 1], {n, 120}] (* Michael De Vlieger, Mar 26 2015 *)

Prog

(PARI) a(n) = numdiv(2^n-1); \\ Michel Marcus, Dec 15 2013
(Magma) [DivisorSigma(0, 2^n - 1): n in [1..100]]; // Vincenzo Librandi, Mar 27 2015
(Python)
from sympy import divisor_count
def A046801(n): return divisor_count((1<<n)-1) # Chai Wah Wu, Mar 13 2023

Crossrefs

Cf. A000043 (n such that a(n) = 2), A000225 (2^n-1).

Sequence in context: A107067 A331580 A320389 * A348717 A316437 A137502

Adjacent sequences: A046798 A046799 A046800 * A046802 A046803 A046804

Keyword

nonn

Author

Labos Elemer

Extensions

Typo in example fixed by Reinhard Zumkeller, May 15 2010

a(0) removed by J. Lowell, Mar 26 2015

Status

approved