[seqfan] A064169

[Tomasz Ordowski]

Dear SeqFans,

I have an interesting conjecture and a related question.

Let H(n) = 1/1 + 1/2 + ... + 1/n is the n-th Harmonic number.
Let N(n) = Numerator(H(n)) and let D(n) = Denominator(H(n)).

The conjecture: For n > 2,
N(n-2) == D(n-2) (mod n) if and only f n is a prime.

The question: Is, by Wolstenholme's theorem,
if p is an odd prime, then N(p-2) == D(p-2) (mod p) ?

Maybe someone knows the answer.

Best regards,

Thomas
_________________________
https://arxiv.org/abs/1111.3057
https://oeis.org/history/view?seq=A064169&v=61
https://en.wikipedia.org/wiki/Wolstenholme%27s_theorem
http://mathworld.wolfram.com/WolstenholmesTheorem.html