A080400 Largest squarefree number dividing phi(n).

1, 1, 2, 2, 2, 2, 6, 2, 6, 2, 10, 2, 6, 6, 2, 2, 2, 6, 6, 2, 6, 10, 22, 2, 10, 6, 6, 6, 14, 2, 30, 2, 10, 2, 6, 6, 6, 6, 6, 2, 10, 6, 42, 10, 6, 22, 46, 2, 42, 10, 2, 6, 26, 6, 10, 6, 6, 14, 58, 2, 30, 30, 6, 2, 6, 10, 66, 2, 22, 6, 70, 6, 6, 6, 10, 6, 30, 6, 78, 2, 6, 10, 82, 6, 2, 42, 14, 10, 22

Offset: 1

Author

Labos Elemer, Mar 19 2003

Keywords

• nonn

Comments

Also largest squarefree number dividing Carmichael's lambda, A002322(n). - Antti Karttunen, Jul 17 2017

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A000010, A002322, A007947, A034380, A289624.

Programs

Mathematica

Table[Max[Select[Divisors[EulerPhi[n]],SquareFreeQ]],{n,90}] (* Harvey P. Dale, Jul 05 2012 *)
a[n_] := Times @@ FactorInteger[EulerPhi[n]][[;; , 1]]; Array[a, 100] (* Amiram Eldar, Jun 18 2022 *)

PARI

A080400(n) = factorback(factorint(eulerphi(n))[, 1]); \\ Antti Karttunen & David A. Corneth, Jul 16 2017

Formula

a(n) = A007947(A000010(n)).

a(m * n) = A007947(a(m) * a(n)) if gcd(m, n) = 1. - David A. Corneth, Jul 16 2017

a(n) = A007947(A002322(n)). - Antti Karttunen, Jul 17 2017