

A225680


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


4



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
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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



