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a(n) is the denominator of Sum_{d|n} (-1)^(d+1) / d^2.
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%I #9 Oct 08 2022 15:11:16

%S 1,4,9,16,25,6,49,64,81,50,121,72,169,98,45,256,289,108,361,200,441,

%T 242,529,288,625,338,729,392,841,15,961,1024,1089,578,49,1296,1369,

%U 722,1521,800,1681,147,1849,88,2025,1058,2209,128,2401,2500,2601,1352,2809,243,3025

%N a(n) is the denominator of Sum_{d|n} (-1)^(d+1) / d^2.

%F Denominators of coefficients in expansion of Sum_{k>=1} (-1)^(k+1) * x^k / (k^2 * (1 - x^k)).

%e 1, 3/4, 10/9, 11/16, 26/25, 5/6, 50/49, 43/64, 91/81, 39/50, 122/121, ...

%t Table[Sum[(-1)^(d + 1)/d^2, {d, Divisors[n]}], {n, 1, 55}] // Denominator

%t nmax = 55; CoefficientList[Series[Sum[(-1)^(k + 1) x^k/(k^2 (1 - x^k)), {k, 1, nmax}], {x, 0, nmax}], x] // Denominator // Rest

%o (Python)

%o from sympy import divisors

%o from fractions import Fraction

%o def a(n): return sum(Fraction((-1)**(d+1), d*d) for d in divisors(n, generator=True)).denominator

%o print([a(n) for n in range(1, 56)]) # _Michael S. Branicky_, Oct 03 2022

%o (PARI) a(n) = denominator(sumdiv(n, d, (-1)^(d+1)/d^2)); \\ _Michel Marcus_, Oct 03 2022

%Y Cf. A017668, A064027, A098988, A321543, A334580, A357555 (numerators).

%K nonn,frac

%O 1,2

%A _Ilya Gutkovskiy_, Oct 03 2022