A245047 Numbers n where phi(n)|n or tau(n)|n.

1, 2, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 40, 48, 54, 56, 60, 64, 72, 80, 84, 88, 96, 104, 108, 128, 132, 136, 144, 152, 156, 162, 180, 184, 192, 204, 216, 225, 228, 232, 240, 248, 252, 256, 276, 288, 296, 324, 328, 344, 348, 360, 372, 376, 384, 396, 424, 432, 441, 444, 448, 450

Offset: 1

Author

Reinhard Muehlfeld, Jul 13 2014

Keywords

• nonn

Comments

Phi(n) is Euler totient function (A000010); tau(n) is the number of divisors of n (A000005).

Union of A007694 and A033950. - Michel Marcus, Jul 15 2014

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000005, A000010, A007694, A033950, A235353.

Programs

Maple

select(t -> (t mod numtheory:-phi(t) = 0) or (t mod numtheory:-tau(t) = 0), [$1..1000]); # Robert Israel, Jul 15 2014

Mathematica

Select[Range[500],AnyTrue[{#/EulerPhi[#],#/DivisorSigma[0,#]},IntegerQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 12 2020 *)

PARI

isok(n) = !((n % eulerphi(n)) && (n % numdiv(n))); \\ Michel Marcus, Jul 15 2014