[seqfan] A sequence characterizing the irregular primes, A000928.

Peter Luschny peter.luschny at googlemail.com
Mon Jun 25 09:27:11 CEST 2012

A prime is irregular if and only if the integer

    Sum_{j=1..p-1} cot^(r)(j*Pi/p)*cot(j*Pi/p)

is divisible by p for some even r <= p-5.

The sequence of these r's would be a nice addition to OEIS
in my opinion. (I do not know if these r's are unique; if not
one could choose the lowest one.) It does not seem to be as easy
as it looks at first glance. All I know is the pair (p,r) = (37,30).
Perhaps someone can take up this idea with more success?

Cheers, Peter


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