OFFSET
1,2
FORMULA
a(n) = Product_{p=primes} (Sum_{k=0..2*b(n, p)} p^(n*k)*(-1)^k), where p^b(n, p) is the highest power of p dividing n.
From Seiichi Manyama, May 18 2024: (Start)
a(n) = Sum_{1 <= x_1, x_2, ... , x_n <= n} ( n/gcd(x_1, x_2, ... , x_n, n) )^n.
a(n) = Sum_{d|n} mu(n/d) * (n/d)^n * sigma_{2*n}(d). (End)
EXAMPLE
sigma_4(4)/sigma_2(4) =
(1 + 2^4 + 4^4)/(1 + 2^2 + 4^2) = 13.
MATHEMATICA
Table[DivisorSigma[2n, n^2]/DivisorSigma[n, n^2], {n, 10}] (* Ryan Propper, Apr 03 2007 *)
PROG
(PARI) a(n) = sigma(n^2, 2*n)/sigma(n^2, n); \\ Michel Marcus, Sep 06 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Jun 28 2005
EXTENSIONS
More terms from Ryan Propper, Apr 03 2007
More terms from Michel Marcus, Sep 06 2019
STATUS
approved