[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.
More information about the SeqFan
mailing list