

A109395


Denominator of phi(n)/n = Prod_{pn} (11/p); phi(n)=A000010(n), the Euler totient function.


12



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, 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, 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
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OFFSET

1,2


COMMENTS

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(q1).  Franz Vrabec, Aug 30 2005


LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000


FORMULA

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


EXAMPLE

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


MATHEMATICA

Table[Denominator[EulerPhi[n]/n], {n, 81}] (* Alonso del Arte, Sep 03 2011 *)


PROG

(PARI) a(n)=n/gcd(n, eulerphi(n)) \\ Charles R Greathouse IV, Feb 20 2013


CROSSREFS

Cf. A076512 for the numerator.
Sequence in context: A197862 A006530 A102095 * A145254 A163457 A285708
Adjacent sequences: A109392 A109393 A109394 * A109396 A109397 A109398


KEYWORD

nonn,frac


AUTHOR

Franz Vrabec, Aug 26 2005


STATUS

approved



