A328274 - OEIS

A328274

Numbers m such that phi(m) = rad(m)^3, where phi is the Euler totient function (A000010) and rad is the squarefree kernel function (A007947).

%I #5 Oct 10 2019 20:31:06

%S 1,16,648,2500,101250,259308,1542294,3660250,4691556,33734898,

%T 846948966,1877404326,21107677374,39691260010,535377671178,

%U 178726991395974

%N Numbers m such that phi(m) = rad(m)^3, where phi is the Euler totient function (A000010) and rad is the squarefree kernel function (A007947).

%C De Koninck et al. showed that there are 16 terms in this sequence.

%H Jean-Marie De Koninck, Florian Luca and A. Sankaranarayanan, <a href="https://projecteuclid.org/euclid.rmjm/1181069489">Positive integers whose Euler function is a power of their kernel function</a>, Rocky Mountain Journal of Mathematics, Vol. 36, No. 1 (2006), pp. 81-96, <a href="https://www.jeanmariedekoninck.mat.ulaval.ca/fileadmin/jmdk/Documents/Publications/2006_positive_integers_whose_euler_function_is_a_power_of_their_kernel_function.pdf">alternative link</a>.

%e 16 is in the sequence since phi(16) = 8, rad(16) = 2 and 8 = 2^3.

%t rad[n_] := Times @@ First /@ FactorInteger[n]; aQ[n_] := EulerPhi[n] == rad[n]^3; Select[Range[5*10^6], aQ]

%Y Cf. A000010, A007947, A105261, A211413, A328275, A328276.

%K nonn,fini,full

%O 1,2

%A _Amiram Eldar_, Oct 10 2019