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

0,1

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).

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

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

Mathematica

Total[#^Range[0, 20]&/@Divisors[40]] (* Vincenzo Librandi, Apr 17 2014 *)

Prog

(Magma) [&+[Divisors(40)[i]^n: i in [1..8]]: n in [0..20]]; // Vincenzo Librandi, Apr 17 2014
(PARI) vector(30, n, sigma(40, n-1)) \\ Colin Barker, May 03 2014

Crossrefs

Sequence in context: A345876 A295623 A319174 * A116149 A184709 A190943

Adjacent sequences: A034664 A034665 A034666 * A034668 A034669 A034670

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved