A034674 - OEIS

%I #23 Sep 08 2022 08:44:52

%S 8,255,21845,2396745,286331153,35468117025,4467856773185,

%T 567382630219905,72340172838076673,9241421688590303745,

%U 1181745669222511412225,151189550474521284184065,19347536633519984760328193

%N Sum of n-th powers of divisors of 128.

%H T. D. Noe, <a href="/A034674/b034674.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. Cites this sequence.

%F a(n) = (2^(8*n) - 1)/(2^n - 1). Exp( Sum_{n >= 1} a(n)*x^n/n ) = 1 + 255*x + 43435*x^2 + ... is the o.g.f. for the 7th subdiagonal of triangle A022166, essentially A022190. - _Peter Bala_, Apr 07 2015

%t Total[#^Range[0, 20]&/@Divisors[128]] (* _Vincenzo Librandi_, Apr 17 2014 *)

%o (Magma) [DivisorSigma(n, 128): n in [0..20]]; // _Vincenzo Librandi_, Apr 17 2014

%Y Cf. A022166, A022190.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_