(MAGMAMagma) [Denominator(Numerator(Bernoulli(n-1))/n + Denominator(Bernoulli(n-1))/n^2): n in [1..70]]; // Vincenzo Librandi, Jul 14 2019
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Table[Denominator[Numerator[BernoulliB[n - 1]] / n + Denominator[ BernoulliB[ n - 1]] / n^2], {n, 70}] (* Vincenzo Librandi, Jul 14 2019 *)
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Theorem 2. If n is a prime or a Carmichael number, then a(n) = A326690(n) = denominator of (Sum_{prime p | n} 1/p - 1/n). The proof is a generalization of that of Theorem 1. (Note that Theorem 2 implies Theorem 1, since if n is prime, then (Sum_{prime p | n} 1/p - 1/n) = 1/n - 1/n = 0, /1, so a(p) = A326690(n) = 1.) For n a prime or a Carmichael number, an application of Theorem 2 is to compute computing a(n) without calculating Bernoulli numbers(n-1) which may be huge; see A309268 and A326690. - Jonathan Sondow, Jul 19 2019
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