cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A366661 Number of divisors of 9^n-1.

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%I A366661 #8 Jan 07 2024 15:46:54
%S A366661 4,10,16,24,24,80,16,112,128,180,64,384,16,160,768,256,128,1280,64,
%T A366661 864,768,640,32,14336,384,160,4096,1536,256,23040,128,576,2048,1280,
%U A366661 768,12288,128,640,12288,16128,128,61440,32,12288,196608,320,512,131072,2048
%N A366661 Number of divisors of 9^n-1.
%H A366661 Max Alekseyev, <a href="/A366661/b366661.txt">Table of n, a(n) for n = 1..690</a>
%F A366661 a(n) = sigma0(9^n-1) = A000005(A024101(n)).
%F A366661 a(n) = A366575(2*n) = A366575(n) * A366577(n) * (4 + A007814(n)) / (2 * (3 + A007814(n))). - _Max Alekseyev_, Jan 07 2024
%e A366661 a(2)=10 because 9^2-1 has divisors {1, 2, 4, 5, 8, 10, 16, 20, 40, 80}.
%p A366661 a:=n->numtheory[tau](9^n-1):
%p A366661 seq(a(n), n=1..100);
%t A366661 DivisorSigma[0, 9^Range[100]-1]
%o A366661 (PARI) a(n) = numdiv(9^n-1);
%Y A366661 Cf. A024101, A000005, A057952, A366660, A366662, A366663.
%Y A366661 Cf. A046801, A366575, A366602, A366612, A366621, A366633, A366652, A070528, A366683, A366709.
%K A366661 nonn
%O A366661 1,1
%A A366661 _Sean A. Irvine_, Oct 15 2023