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A109395 Denominator of phi(n)/n = Prod_{p|n} (1-1/p); phi(n)=A000010(n), the Euler totient function. 14


%S 1,2,3,2,5,3,7,2,3,5,11,3,13,7,15,2,17,3,19,5,7,11,23,3,5,13,3,7,29,

%T 15,31,2,33,17,35,3,37,19,13,5,41,7,43,11,15,23,47,3,7,5,51,13,53,3,

%U 11,7,19,29,59,15,61,31,7,2,65,33,67,17,69,35,71,3,73,37,15,19,77,13,79,5,3

%N Denominator of phi(n)/n = Prod_{p|n} (1-1/p); phi(n)=A000010(n), the Euler totient function.

%C a(n)=2 iff n=2^k (k>0); otherwise a(n) is odd. If p is prime, a(p)=p; the converse is false, e.g.: a(15)=15. It is remarkable that this sequence often coincides with A006530, the largest prime P dividing n. Theorem: a(n)=P if and only if for every prime p<P in n there is some prime q in n with p|(q-1). - _Franz Vrabec_, Aug 30 2005

%H T. D. Noe, <a href="/A109395/b109395.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n)=n/gcd(n, phi(n))=n/A009195(n).

%e a(10)=10/gcd(10,phi(10))=10/gcd(10,4)=10/2=5.

%t Table[Denominator[EulerPhi[n]/n], {n, 81}] (* _Alonso del Arte_, Sep 03 2011 *)

%o (PARI) a(n)=n/gcd(n,eulerphi(n)) \\ _Charles R Greathouse IV_, Feb 20 2013

%Y Cf. A076512 for the numerator.

%K nonn,frac

%O 1,2

%A _Franz Vrabec_, Aug 26 2005

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Last modified October 21 09:43 EDT 2018. Contains 316413 sequences. (Running on oeis4.)