A225680 Denominators of phi(k)/k, as k runs through the squarefree numbers (A005117).

1, 2, 3, 5, 3, 7, 5, 11, 13, 7, 15, 17, 19, 7, 11, 23, 13, 29, 15, 31, 33, 17, 35, 37, 19, 13, 41, 7, 43, 23, 47, 51, 53, 11, 19, 29, 59, 61, 31, 65, 33, 67, 69, 35, 71, 73, 37, 77, 13, 79, 41, 83, 85, 43, 87, 89, 91, 31, 47, 95, 97, 101, 51, 103, 35, 53, 107

Offset

1,2

Comments

To every fraction taken by the arithmetical function m -> phi(m)/m there is exactly one n such that A225679(n)/A225680(n) is equal to it.

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Formula

a(n)=A005117(n)/gcd(A000010(A005117(n)),A005117(n)).

Example

A005117(5)=6, phi(6)/6=2/6=1/3, so a(5)=3.

Mathematica

s = Select[Range[200], SquareFreeQ]; Denominator[EulerPhi[s]/s] (* T. D. Noe, May 13 2013 *)

Prog

(PARI) lista(nn) = apply(x->(denominator(eulerphi(x)/x)), Vec(select(issquarefree, [1..nn], 1))); \\ Michel Marcus, Feb 22 2021

Crossrefs

Cf. A225679 (numerators).

Sequence in context: A341643 A073482 A318411 * A346091 A107685 A161984

Adjacent sequences: A225677 A225678 A225679 * A225681 A225682 A225683

Keyword

nonn,frac,easy

Author

Franz Vrabec, May 12 2013

Status

approved