A366606 Number of divisors of 4^n+1.

2, 2, 2, 4, 2, 6, 4, 8, 2, 16, 4, 8, 8, 16, 4, 48, 4, 16, 16, 16, 4, 64, 8, 32, 8, 64, 8, 64, 8, 8, 16, 32, 4, 64, 12, 96, 32, 32, 16, 768, 8, 32, 32, 32, 16, 1536, 4, 16, 8, 64, 64, 512, 4, 16, 64, 96, 32, 256, 8, 128, 64, 64, 16, 1024, 4, 768, 128, 64, 16

Offset

0,1

Links

Max Alekseyev, Table of n, a(n) for n = 0..561

Formula

a(n) = sigma0(4^n+1) = A000005(A052539(n)).

a(n) = A046798(2*n). - Max Alekseyev, Jan 08 2024

Example

a(3)=4 because 4^3+1 has divisors {1, 5, 13, 65}.

Maple

a:=n->numtheory[tau](4^n+1):
seq(a(n), n=0..100);

Mathematica

DivisorSigma[0, 4^Range[0, 100]+1] (* Paolo Xausa, Oct 14 2023 *)

Prog

(PARI) a(n) = numdiv(4^n+1);
(Python)
from sympy import divisor_count
def A366606(n): return divisor_count((1<<(n<<1))+1) # Chai Wah Wu, Oct 14 2023

Crossrefs

Cf. A000005, A052539, A057940, A274903, A366602, A366605, A366607, A366608, A366609.

Cf. A046798, A366577, A366616, A366628, A366637, A366656, A366665, A344897, A366688, A366714.

Sequence in context: A054712 A345067 A066243 * A278242 A035580 A135293

Adjacent sequences: A366603 A366604 A366605 * A366607 A366608 A366609

Keyword

nonn

Author

Sean A. Irvine, Oct 14 2023

Status

approved