[seqfan] After Wolstenholme and Leudesdorf

Tomasz Ordowski tomaszordowski at gmail.com
Tue Aug 13 07:24:02 CEST 2019

Dear SeqFans,

I formulated three interesting conjectures.

Let a(n) = Numerator(Sum_{1<=k<=n, (k,n)=1} 1/k).
Let b(n) = Numerator(Sum_{1<=k<=n, (k,n)=1} 1/k^2).

Conjecture 1. If, for some e > 0, n^e | a(n), then n^{e-1} | b(n).
Conjecture 2. For odd n, n^e | a(n) if and only if n^{e-1} | b(n).
Conjecture 3. There are no numbers n > 1 such that n^4 | a(n).

Amiram Eldar tested my conjectures to some extent.
I am asking for proofs or counterexamples.

Best regards,

Thomas Ordowski
a(n) = A093600(n),
b(n) is not in OEIS.

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