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A357555 a(n) is the numerator of Sum_{d|n} (-1)^(d+1) / d^2.

%I A357555 #10 Oct 08 2022 15:11:12
%S A357555 1,3,10,11,26,5,50,43,91,39,122,55,170,75,52,171,290,91,362,143,500,
%T A357555 183,530,215,651,255,820,275,842,13,962,683,1220,435,52,1001,1370,543,
%U A357555 1700,559,1682,125,1850,61,2366,795,2210,95,2451,1953,2900,935,2810,205,3172
%N A357555 a(n) is the numerator of Sum_{d|n} (-1)^(d+1) / d^2.
%F A357555 Numerators of coefficients in expansion of Sum_{k>=1} (-1)^(k+1) * x^k / (k^2 * (1 - x^k)).
%e A357555 1, 3/4, 10/9, 11/16, 26/25, 5/6, 50/49, 43/64, 91/81, 39/50, 122/121, ...
%t A357555 Table[Sum[(-1)^(d + 1)/d^2, {d, Divisors[n]}], {n, 1, 55}] // Numerator
%t A357555 nmax = 55; CoefficientList[Series[Sum[(-1)^(k + 1) x^k/(k^2 (1 - x^k)), {k, 1, nmax}], {x, 0, nmax}], x] // Numerator // Rest
%o A357555 (Python)
%o A357555 from sympy import divisors
%o A357555 from fractions import Fraction
%o A357555 def a(n): return sum(Fraction((-1)**(d+1), d*d) for d in divisors(n, generator=True)).numerator
%o A357555 print([a(n) for n in range(1, 56)]) # _Michael S. Branicky_, Oct 03 2022
%o A357555 (PARI) a(n) = numerator(sumdiv(n, d, (-1)^(d+1)/d^2)); \\ _Michel Marcus_, Oct 03 2022
%Y A357555 Cf. A017667, A064027, A098987, A119682, A321543, A357556 (denominators).
%K A357555 nonn,frac
%O A357555 1,2
%A A357555 _Ilya Gutkovskiy_, Oct 03 2022