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%I #30 Sep 08 2022 08:44:51
%S 4,15,85,585,4369,33825,266305,2113665,16843009,134480385,1074791425,
%T 8594130945,68736258049,549822930945,4398314962945,35185445863425,
%U 281479271743489,2251816993685505,18014467229220865
%N Sum of n-th powers of divisors of 8.
%C Conjecture: No primes in this sequence (checked for first 10000 terms). [_Artur Jasinski_, Sep 23 2008]
%C All terms are composite because a(n) = (1 + 2^n)*(1 + 4^n). [_T. D. Noe_, Apr 26 2010]
%H T. D. Noe, <a href="/A034496/b034496.txt">Table of n, a(n) for n = 0..200</a>
%H Quynh Nguyen, Jean Pedersen, and Hien T. Vu, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL19/Pedersen/pedersen2.html">New Integer Sequences Arising From 3-Period Folding Numbers</a>, Vol. 19 (2016), Article 16.3.1. See Table 1.
%F G.f.: (4 - 45*x + 140*x^2 - 120*x^3)/((1 - 8*x)*(1 - 4*x)*(1 - 2*x)*(1 - x)). [_Bruno Berselli_, Apr 17 2014]
%F a(n) = (2^(4*n) - 1)/( 2^n - 1) = 1 + 2^n + 4^n + 8^n. Exp( Sum_{n >= 1} a(n)*x^n/n ) = 1 + 15*x + 155*x^2 + 1395*x^3 + ... is the o.g.f. for the 3rd subdiagonal of triangle A022166, essentially A006096. - _Peter Bala_, Apr 07 2015
%t Total[#^Range[0, 20]&/@Divisors[8]] (* _Vincenzo Librandi_, Apr 17 2014 *)
%t DivisorSigma[Range[0,20],8] (* _Harvey P. Dale_, May 16 2020 *)
%o (Sage) [sigma(8,n) for n in range(0,19)] # _Zerinvary Lajos_, Jun 04 2009
%o (PARI) a(n)=sigma(8, n) \\ _Charles R Greathouse IV_, May 16 2011
%o (Magma) [DivisorSigma(n,8): n in [0..20]]; // _Vincenzo Librandi_, Apr 17 2014
%Y Cf. A006096, A022166.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_.
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