OFFSET
1,1
COMMENTS
EXAMPLE
phi(54) = 18, tau(54) = 8, phi(54)*tau(54) = 18*8 = 144 = 12^2 but phi(54)/tau(54) = 9/4 = (3/2)^2 is not the square of an integer, hence 54 is a term.
phi(1026) = 324, tau(1026) = 16, phi(1026)*tau(1026) = 324*16 = 5184 = 72^2 but phi(1026)/tau(1026) = 324/16 = 81/4 = (9/2)^2 is not the square of an integer, hence 1026 is another term.
MAPLE
with(numtheory): filter:= r -> phi(r)/tau(r) <> floor(phi(r)/tau(r)) and issqr(phi(r)*tau(r)) : select(filter, [$1..50000]);
MATHEMATICA
Select[Range[10^5], IntegerQ /@ Sqrt[{(e = EulerPhi[#])*(d = DivisorSigma[0, #]), e/d}] == {True, False} &] (* Amiram Eldar, Feb 24 2021 *)
PROG
(PARI) isok(m) = my(x=eulerphi(m), y = numdiv(m)); issquare(x*y) && (denominator(x/y) != 1); \\ Michel Marcus, Feb 24 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Bernard Schott, Feb 24 2021
STATUS
approved