A357556 a(n) is the denominator of Sum_{d|n} (-1)^(d+1) / d^2.
1, 4, 9, 16, 25, 6, 49, 64, 81, 50, 121, 72, 169, 98, 45, 256, 289, 108, 361, 200, 441, 242, 529, 288, 625, 338, 729, 392, 841, 15, 961, 1024, 1089, 578, 49, 1296, 1369, 722, 1521, 800, 1681, 147, 1849, 88, 2025, 1058, 2209, 128, 2401, 2500, 2601, 1352, 2809, 243, 3025
Offset: 1
Examples
1, 3/4, 10/9, 11/16, 26/25, 5/6, 50/49, 43/64, 91/81, 39/50, 122/121, ...
Programs
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Mathematica
Table[Sum[(-1)^(d + 1)/d^2, {d, Divisors[n]}], {n, 1, 55}] // Denominator nmax = 55; CoefficientList[Series[Sum[(-1)^(k + 1) x^k/(k^2 (1 - x^k)), {k, 1, nmax}], {x, 0, nmax}], x] // Denominator // Rest -
PARI
a(n) = denominator(sumdiv(n, d, (-1)^(d+1)/d^2)); \\ Michel Marcus, Oct 03 2022
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Python
from sympy import divisors from fractions import Fraction def a(n): return sum(Fraction((-1)**(d+1), d*d) for d in divisors(n, generator=True)).denominator print([a(n) for n in range(1, 56)]) # Michael S. Branicky, Oct 03 2022
Formula
Denominators of coefficients in expansion of Sum_{k>=1} (-1)^(k+1) * x^k / (k^2 * (1 - x^k)).