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A109395 Denominator of phi(n)/n = Prod_{p|n} (1-1/p); phi(n)=A000010(n), the Euler totient function. 9
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 (list; graph; refs; listen; history; text; internal format)
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|(q-1). - 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 A072593

Adjacent sequences:  A109392 A109393 A109394 * A109396 A109397 A109398

KEYWORD

nonn,frac

AUTHOR

Franz Vrabec, Aug 26 2005

STATUS

approved

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Last modified December 4 11:13 EST 2016. Contains 278750 sequences.