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).

1, 16, 648, 2500, 101250, 259308, 1542294, 3660250, 4691556, 33734898, 846948966, 1877404326, 21107677374, 39691260010, 535377671178, 178726991395974

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..16.

Jean-Marie De Koninck, Florian Luca and A. Sankaranarayanan, Positive integers whose Euler function is a power of their kernel function, Rocky Mountain Journal of Mathematics, Vol. 36, No. 1 (2006), pp. 81-96, alternative link.

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A128048 A197670 A162546 * A249950 A334734 A220298

Adjacent sequences: A328271 A328272 A328273 * A328275 A328276 A328277

Keyword

nonn,fini,full

Author

Amiram Eldar, Oct 10 2019

Status

approved