OFFSET
1,2
COMMENTS
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..387
M. Sugunamma, Certain results concerning sigma_k(n) and phi_k(n), Annales Polonici Mathematici, Vol. 8, No. 2 (1960), pp. 173-176.
Eric Weisstein's World of Mathematics, Divisor Function.
FORMULA
G.f.: Sum_{k>=1} k^(k-1)*x^k/(1 - (k*x)^k). - Ilya Gutkovskiy, Nov 02 2018
L.g.f.: -log(Product_{k>=1} (1 - (k*x)^k)^(1/k^2)) = Sum_{k>=1} a(k)*x^k/k. - Seiichi Manyama, Jun 23 2019
EXAMPLE
a(6) = 1^5 + 2^5 + 3^5 + 6^5 = 1 + 32 + 243 + 7776 = 8052.
MATHEMATICA
Table[Total[Divisors[n]^(n-1)], {n, 18}] (* T. D. Noe, Oct 25 2006 *)
Table[DivisorSigma[n-1, n], {n, 1, 20}] (* G. C. Greubel, Nov 02 2018 *)
PROG
(Sage) [sigma(n, (n-1))for n in range(1, 19)] # Zerinvary Lajos, Jun 04 2009
(PARI) a(n) = sigma(n, n-1); \\ Michel Marcus, Nov 07 2017
(PARI) N=20; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-(k*x)^k)^(1/k^2))))) \\ Seiichi Manyama, Jun 23 2019
(Magma) [DivisorSigma(n-1, n): n in [1..20]]; // G. C. Greubel, Nov 02 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, May 22 2003
EXTENSIONS
Corrected by T. D. Noe, Oct 25 2006
STATUS
approved