login
A366661
Number of divisors of 9^n-1.
12
4, 10, 16, 24, 24, 80, 16, 112, 128, 180, 64, 384, 16, 160, 768, 256, 128, 1280, 64, 864, 768, 640, 32, 14336, 384, 160, 4096, 1536, 256, 23040, 128, 576, 2048, 1280, 768, 12288, 128, 640, 12288, 16128, 128, 61440, 32, 12288, 196608, 320, 512, 131072, 2048
OFFSET
1,1
LINKS
FORMULA
a(n) = sigma0(9^n-1) = A000005(A024101(n)).
a(n) = A366575(2*n) = A366575(n) * A366577(n) * (4 + A007814(n)) / (2 * (3 + A007814(n))). - Max Alekseyev, Jan 07 2024
EXAMPLE
a(2)=10 because 9^2-1 has divisors {1, 2, 4, 5, 8, 10, 16, 20, 40, 80}.
MAPLE
a:=n->numtheory[tau](9^n-1):
seq(a(n), n=1..100);
MATHEMATICA
DivisorSigma[0, 9^Range[100]-1]
PROG
(PARI) a(n) = numdiv(9^n-1);
KEYWORD
nonn
AUTHOR
Sean A. Irvine, Oct 15 2023
STATUS
approved