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

Author

Franz Vrabec, May 12 2013

Keywords

• nonn
• frac
• easy

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.

Examples

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

Links

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

Crossrefs

Cf. A225679 (numerators).

Programs

Mathematica

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

PARI

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

Formula

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