OFFSET
1,1
COMMENTS
Apparently, these is a single x, 6, such that uphi(x)/x = 1/3.
LINKS
Max Alekseyev, Table of n, a(n) for n = 1..68
Tomohiro Yamada, An analog of perfect numbers involving the unitary totient function, arXiv:1806.00647 [math.NT], 2018.
EXAMPLE
uphi(3) = 2 so uphi(3)/3 = 2/3;
uphi(36) = 24 so uphi(36)/36 = 2/3.
MATHEMATICA
uphi[n_] := Times @@ ((First[#]^Last[#] - 1) & /@ FactorInteger[n]); uphi[1] = 1; Select[Range[200000], uphi[#] == 2*#/3 &] (* Amiram Eldar, Oct 21 2025 *)
PROG
(PARI) uphi(n) = my(f=factor(n)~); prod(i=1, #f, f[1, i]^f[2, i]-1);
isok(n) = uphi(n) == 2*n/3; \\ Michel Marcus, Oct 21 2025
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Marcus, Jun 08 2018
EXTENSIONS
Missing a(21), a(23), a(25), a(28)-a(29) inserted by Max Alekseyev, Oct 20 2025
STATUS
approved
