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A108223
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a(n) = sigma_{2n}(n^2)/sigma_n(n^2), where sigma_n(m) = Sum_{d|m} d^n.
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2
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1, 13, 703, 61681, 9762501, 2140365529, 678222249307, 280379743338241, 150087010086914941, 99902428887422922553, 81402749386554449442711, 79477293980103609858493681, 91733330193268313783293023757, 123469159731637675342948027295569, 191751045863140709562160603031808243
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OFFSET
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1,2
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LINKS
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FORMULA
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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.
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)
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EXAMPLE
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sigma_4(4)/sigma_2(4) =
(1 + 2^4 + 4^4)/(1 + 2^2 + 4^2) = 13.
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MATHEMATICA
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Table[DivisorSigma[2n, n^2]/DivisorSigma[n, n^2], {n, 10}] (* Ryan Propper, Apr 03 2007 *)
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PROG
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(PARI) a(n) = sigma(n^2, 2*n)/sigma(n^2, n); \\ Michel Marcus, Sep 06 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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