A034667 Sum of n-th powers of divisors of 40.
8, 90, 2210, 73710, 2734994, 105736950, 4161281930, 165132191790, 6579317233634, 262657136433510, 10496011084557050, 419635308642959070, 16781313068980398674, 671170570551043634070, 26845184104404418478570, 1073774593035215963441550
Offset: 0
Links
- T. D. Noe, Table of n, a(n) for n=0..200
- Index entries for linear recurrences with constant coefficients, signature (90,-2945,46620,-396564,1864800,-4712000,5760000,-2560000).
Programs
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Magma
[&+[Divisors(40)[i]^n: i in [1..8]]: n in [0..20]]; // Vincenzo Librandi, Apr 17 2014
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Maple
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
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Mathematica
Total[#^Range[0, 20]&/@Divisors[40]] (* Vincenzo Librandi, Apr 17 2014 *)
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PARI
vector(30, n, sigma(40, n-1)) \\ Colin Barker, May 03 2014
Formula
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
a(n) = 1+2^n+4^n+5^n+8^n+10^n+20^n+40^n. - Wesley Ivan Hurt, Oct 23 2014
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