A034669 Sum of n-th powers of divisors of 56.
8, 120, 4250, 201240, 10494338, 568530600, 31330783250, 1740696128760, 97096611969218, 5426768739979080, 303601976474731250, 16993404958986493080, 951398288846993188898, 53271799678887170275560, 2983038689530691785543250, 167045068491414861803398200
Offset: 0
Links
- T. D. Noe, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (120,-5075,100080,-1023828,5604480,-15915200,21073920,-9834496).
Crossrefs
Cf. A018265 (divisors of 56).
Programs
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Magma
[DivisorSigma(n,56): n in [0..15]]; // Vincenzo Librandi, Apr 17 2014
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Mathematica
Total[#^Range[0, 20]&/@Divisors[56]] (* Vincenzo Librandi, Apr 17 2014 *)
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PARI
vector(30, n, sigma(56, n-1)) \\ Colin Barker, May 03 2014
Formula
G.f.: -2*(10536960*x^7 -15915200*x^6 +8406720*x^5 -2047656*x^4 +250200*x^3 -15225*x^2 +420*x -4) / ((x -1)*(2*x -1)*(4*x -1)*(7*x -1)*(8*x -1)*(14*x -1)*(28*x -1)*(56*x -1)). - Colin Barker, May 03 2014