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A366606
Number of divisors of 4^n+1.
10
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
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
KEYWORD
nonn
AUTHOR
Sean A. Irvine, Oct 14 2023
STATUS
approved