Talk:Radical of an integer

Division of Radicals?

Is there a way someone could expand this to include various tasks with radicals, such as division, multiplication, subtraction, addition, fractions, and simplifying fractions? I am currently working through some of those in my Algebra class, and would like more information. God bless, 12.201.82.94 19:21, 11 April 2007 (UTC)

Square-free part

Is the radical the same as the square-free part? I would have said that the radical of 12 was 6 but the square-free part of 12 was 3. Any references? Richard Pinch (talk) 06:49, 2 July 2008 (UTC)

rad(n) is formed by taking the prime factorization n = Π p_i^e_i and replacing each e_i by 1. For example, 360 = 2³×3²×5¹ so rad(360) = 2×3×5=30. The squarefree part is formed by replacing each e_i by e_i mod 2, or equivalently taking the product of only the primes with odd exponents, so for 360 you get 2×5=10. See e.g. OEIS. —David Eppstein (talk) 07:26, 2 July 2008 (UTC)

I thought so, thanks. Richard Pinch (talk) 18:55, 2 July 2008 (UTC)

bad notation

The current formula, rad(n) = product_{ p|n } p is not correct: in this formula, the condition "p prime" is missing. (It is said in the text but IMHO this does not justify to omit it in the formula.)— MFH:Talk 02:49, 12 November 2008 (UTC)

In number theory, certain variables are usually assumed to vary over the prime numbers: $p,q,\varpi$ and often r and s. CRGreathouse (t | c) 22:00, 12 July 2010 (UTC)

Incorrect link to german Wikipedia article

Hi, the link of this article to it's corresponding german wikipedia-article is obviously wrong. Currently it's https://de.wikipedia.org/wiki/Zahlentheoretische_Funktion#Multiplikative_Funktionen, but it should imho be https://de.wikipedia.org/wiki/Radikal_(Mathematik)#In_der_Zahlentheorie. I don't know, how to correct this... Somebody else? — Preceding unsigned comment added by 2A02:908:1B1B:5C20:7515:B304:A66B:8561 (talk) 12:33, 4 November 2019 (UTC)

example

It seems useful to add: rad(n!)=n# 2001:861:3D00:8A80:4AE:A549:713C:C0E8 (talk) 15:47, 3 January 2025 (UTC)