[seqfan] Re: number-theoretic notation

[allouche at math.jussieu.fr]

Dear Ed

Usually the notation p^{\alpha} || n means "divides exactly",
meaning that alpha is the largest power of p such that p^{\alpha}
divides n. Like 2^3 || 24
(here p is prime and alpha an integer)
best
jp


Ed Jeffery <lejeffery7 at gmail.com> a écrit :

> I have been studying an obscure article that, in part, enumerates certain
> classes of subfields, and I want to eventually submit the sequences if they
> are not in OEIS. However, in studying their equations, I noticed that the
> authors used the notation
>
> p | m,
>
> which I take to mean the usual the "prime p divides m" (or with a slash
> through the line to mean the converse), but several times in conjunction
> with that, and often in the same paragraph or sentence, they use the
> notation
>
> p || m.
>
> The two vertical lines I have never seen before as a binary relation in
> number theory. I checked my Hardy & Wright, 5th ed., as well as my old
> Harper Collins mathematics dictionary, and did not find this, and I have
> been searching online all day with no luck. Note that in the article, p
> always denotes a prime, and m is a positive integer.
>
> Does anyone know what that notation means in the number-theoretic context?
>
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