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A034660 Sum of n-th powers of divisors of 12. 7
6, 28, 210, 2044, 22386, 257908, 3037530, 36130444, 431733666, 5170140388, 61978939050, 743375541244, 8918294543346, 107006334784468, 1283997101947770, 15407492847694444, 184887084343023426 (list; graph; refs; listen; history; text; internal format)
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 *)

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 xrange(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

CROSSREFS

Sequence in context: A278015 A169723 A052395 * A206708 A216413 A090898

Adjacent sequences:  A034657 A034658 A034659 * A034661 A034662 A034663

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified May 30 06:51 EDT 2017. Contains 287302 sequences.