A034660 Sum of n-th powers of divisors of 12.

6, 28, 210, 2044, 22386, 257908, 3037530, 36130444, 431733666, 5170140388, 61978939050, 743375541244, 8918294543346, 107006334784468, 1283997101947770, 15407492847694444, 184887084343023426, 2218628050709022148, 26623434909949071690, 319480609006403630044

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• T. D. Noe, Table of n, a(n) for n = 0..200

Programs

Magma

[&+[Divisors(12)[i]^n: i in [1..6]]: n in [0..20]]; // Vincenzo Librandi, Apr 17 2014

Mathematica

a[n_] := Plus@@(Divisors[12]^n)
Total[#^Range[0, 20]&/@Divisors[12]] (* Vincenzo Librandi, Apr 17 2014 *)
DivisorSigma[Range[0,20],12] (* Harvey P. Dale, Sep 17 2019 *)

PARI

a(n)=if(n<0,0,polsym((x-1)*(x-2)*(x-3)*(x-4)*(x-6)*(x-12),n)[n+1])

PARI

a(n)=if(n<0,0,1^n+2^n+3^n+4^n+6^n+12^n)

Python

def a(n): return sum(d**n for d in [1, 2, 3, 4, 6, 12])
print([a(n) for n in range(20)]) # Michael S. Branicky, Jun 28 2021

Sage

[sigma(12,n)for n in range(0,17)] # Zerinvary Lajos, Jun 04 2009

Formula

G.f.: (6 - 140*x + 1148*x^2 - 4200*x^3 + 6888*x^4 - 4032*x^5)/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)*(1-6*x)*(1-12*x)). - Michael Somos, Apr 02 2003