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.
%I A034667 #28 Jul 08 2025 21:26:30 %S A034667 8,90,2210,73710,2734994,105736950,4161281930,165132191790, %T A034667 6579317233634,262657136433510,10496011084557050,419635308642959070, %U A034667 16781313068980398674,671170570551043634070,26845184104404418478570,1073774593035215963441550 %N A034667 Sum of n-th powers of divisors of 40. %H A034667 T. D. Noe, <a href="/A034667/b034667.txt">Table of n, a(n) for n=0..200</a> %H A034667 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (90,-2945,46620,-396564,1864800,-4712000,5760000,-2560000). %F A034667 G.f.: -2*(2880000*x^7 -4712000*x^6 +2797200*x^5 -793128*x^4 +116550*x^3 -8835*x^2 +315*x -4) / ((x -1)*(2*x -1)*(4*x -1)*(5*x -1)*(8*x -1)*(10*x -1)*(20*x -1)*(40*x -1)). - _Colin Barker_, May 03 2014 %F A034667 a(n) = 1+2^n+4^n+5^n+8^n+10^n+20^n+40^n. - _Wesley Ivan Hurt_, Oct 23 2014 %F A034667 a(n) = 90*a(n-1)-2945*a(n-2)+46620*a(n-3)-396564*a(n-4)+1864800*a(n-5)-4712000*a(n-6)+5760000*a(n-7)-2560000*a(n-8). - _Wesley Ivan Hurt_, Oct 23 2014 %p A034667 A034667:=n->1+2^n+4^n+5^n+8^n+10^n+20^n+40^n: seq(A034667(n), n=0..15); # _Wesley Ivan Hurt_, Oct 23 2014 %t A034667 Total[#^Range[0, 20]&/@Divisors[40]] (* _Vincenzo Librandi_, Apr 17 2014 *) %o A034667 (Magma) [&+[Divisors(40)[i]^n: i in [1..8]]: n in [0..20]]; // _Vincenzo Librandi_, Apr 17 2014 %o A034667 (PARI) vector(30, n, sigma(40, n-1)) \\ _Colin Barker_, May 03 2014 %K A034667 nonn,easy %O A034667 0,1 %A A034667 _N. J. A. Sloane_