[seqfan] Conjecture and Problem

[Tomasz Ordowski]

Hello SeqFans!

Let a(n) = Numerator(Sum_{0<k<n, (k,n)=1} 1/k) for n>1, a(1)=1.
Let b(n) = Numerator(Sum_{0<k<n, (k,n)=1} 1/k^2) for n>1, b(1)=1.
Conjecture: If, for some e > 0, n^e | a(n), then n^{e-1} | b(n).
Problem: Are there numbers n > 1 such that n^4 | a(n) ?

How to prove my conjecture and solve my problem?

Best regards,

Thomas Ordowski
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Cf. https://oeis.org/history/view?seq=A290815&v=21
Please pay special attention to the last two comments.