A329859 Numbers k such that k and uphi(k) have the same set of prime divisors, where uphi is the unitary totient function (A047994).

1, 12, 36, 168, 240, 504, 702, 720, 1176, 1200, 1344, 1404, 1620, 3528, 3600, 4032, 4050, 6480, 8100, 9408, 14880, 19656, 22680, 23250, 28080, 28224, 32400, 44640, 46500, 53460, 63882, 65280, 69750, 74400, 113400, 127764, 132678, 133650, 137592, 139500

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..1052 (terms below 5*10^10)

Example

12 is in the sequence since 12 = 2^2 * 3 and uphi(12) = 6 = 2 * 3 both have the same set of prime divisors, {2, 3}.

Mathematica

rad[n_] := Times @@ (First@# & /@ FactorInteger@ n); uphi[1] = 1; uphi[n_] := Times @@ (-1 + Power @@@ FactorInteger[n]); Select[Range[10^5], rad[#] == rad[uphi[#]] &]

Crossrefs

The unitary version of A055744.

Cf. A007947, A027598, A047994.

Sequence in context: A238923 A135178 A278583 * A216381 A085331 A225100

Adjacent sequences: A329856 A329857 A329858 * A329860 A329861 A329862

Keyword

nonn

Author

Amiram Eldar, Nov 22 2019

Status

approved