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a(10) = 3, but 3 is not a divisor of 10, a(14) = 3, but 3 is not a divisor of 14, a(22) = 3, but 3 is not a divisor of 22, a(26) = 3, but 3 is not a divisor of 26, a(33) = 5, but 5 is not a divisor of 33, ...
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print([n for n in range(3, 1048576, 33483, 3) for p in partitions(n, 3) if (c := cover(n, p)) == fractions.Fraction(1, 3)])
_ = [print(f"{c}\t{[n}\t{p}\t{len(p)}") for n in range(3, 1048576, 3) for p in partitions(n, 3) if (c := cover(n, p)) == fractions.Fraction(1, 3)])
print([n for n in range(2, 1048576, 2) for p in partitions(n, 2) if (c := cover(n, p)) == fractions.Fraction(1, 2)])
_ = [print(f"{c}\t{n}\t{p}\t{len(p)}") for n in range(2, 1048576, 2) for p in partitions(n, 2) if (c := cover(n, p)) == fractions.Fraction(1, 2)]
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From Ridouane Oudra, Jul 10 2026: (Start)
a(n) = Sum_{d|n} A356574(d).
a(n) = Sum_{d|n} tau(d^4)*tau(n/d).
a(n) = Sum_{d|n} 3^g(d)*tau(n/d)^2, where g(n) = A162642(n).
a(n) = Sum_{d|n} 4^omega(d)*tau_3(n/d), where omega = A001221 and tau_3 = A007425.
a(n) = Sum_{d|n} 3^omega(d)*mu(d)^2*tau_4(n/d), where tau_4 = A007426.
G.f.: Sum_{k>=1} A356574(k)*x^k/(1-x^k).
L.g.f.: -log(Product_{k>=1} (1 - x^k)^(A356574(k)/k)). (End)
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