login
A373319
Denominator of the asymptotic density of numbers that are unitarily divided by n.
3
1, 4, 9, 8, 25, 18, 49, 16, 27, 25, 121, 36, 169, 98, 225, 32, 289, 54, 361, 50, 147, 242, 529, 72, 125, 169, 81, 196, 841, 225, 961, 64, 1089, 289, 1225, 108, 1369, 722, 507, 100, 1681, 147, 1849, 484, 675, 1058, 2209, 144, 343, 125, 2601, 338, 2809, 162, 605
OFFSET
1,2
LINKS
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
Cf. A003277, A373318 (numerators), A373320.
Sequence in context: A355012 A280286 A268597 * A253560 A050399 A072995
KEYWORD
nonn,easy,frac
AUTHOR
Amiram Eldar, Jun 01 2024
STATUS
approved