OFFSET
1,2
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Unitary Divisor.
Wikipedia, Unitary divisor.
FORMULA
a(n) = n^2 if and only if n is a cyclic number (A003277).
EXAMPLE
Fractions begin with: 1, 1/4, 2/9, 1/8, 4/25, 1/18, 6/49, 1/16, 2/27, 1/25, 10/121, 1/36, ...
For n = 2, the numbers that are unitarily divided by 2 are the numbers of the form 4*k+2 whose asymptotic density is 1/4. Therefore a(2) = denominator(1/4) = 4.
MATHEMATICA
a[n_] := Denominator[EulerPhi[n]/n^2]; Array[a, 100]
PROG
(PARI) a(n) = denominator(eulerphi(n)/n^2);
(PARI) for(n=1, 100, print1(denominator(direuler(p=2, n, (1-X/p^2)/(1-X/p))[n]), ", ")) \\ Vaclav Kotesovec, Jun 01 2024
CROSSREFS
KEYWORD
nonn,easy,frac
AUTHOR
Amiram Eldar, Jun 01 2024
STATUS
approved