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

0,1

Links

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

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

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 *)

Prog

(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)
(Sage) [sigma(12, n)for n in range(0, 17)] # Zerinvary Lajos, Jun 04 2009
(Magma) [&+[Divisors(12)[i]^n: i in [1..6]]: n in [0..20]]; // Vincenzo Librandi, Apr 17 2014
(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

Crossrefs

Sequence in context: A345002 A169723 A052395 * A347770 A206708 A336565

Adjacent sequences: A034657 A034658 A034659 * A034661 A034662 A034663

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved